
496 F.3d 791 (2007)
UNITED STATES of America, Plaintiff-Appellee,
v.
Anthony WOMACK, also known as Bigman, also known as Bigs, Defendant-Appellant.
No. 06-4266.
United States Court of Appeals, Seventh Circuit.
Argued June 7, 2007.
Decided August 3, 2007.
*792 *793 Ranley R. Killian, Jr., Office of the United States Attorney, Criminal Division, Fairview Heights, IL, Michael C. Carr (argued), Office of the U.S. Attorney, Benton, IL, for Plaintiff-Appellee.
Irl B. Baris (argued), Baris Law Firm, St. Louis, MO, for Defendant-Appellant.
Before BAUER, ROVNER, and SYKES, Circuit Judges.
BAUER, Circuit Judge.
Anthony Womack was arrested when he was indicted, with several other individuals, for conspiracy to possess with intent to distribute and distribution of cocaine in excess of five kilograms, in violation of 21 U.S.C. §§ 841 and 846. At his trial, the jury heard testimony from several witnesses about Womack's role in a cocainedistribution operation led by Carl Parker and Roosevelt Turner in the St. Louis metropolitan area; Turner supplied Womack with cocaine, which Womack then sold to others. The jury also heard from witnesses regarding their cocaine purchases from Womack and their knowledge of Womack's other drug deals.
The jury convicted Womack of both conspiracy to possess with intent to distribute and distribution of cocaine, finding by special verdict that the amount of cocaine was in excess of five kilograms. The district court sentenced Womack to 151 months' imprisonment.
*794 Womack appeals both his conviction and sentence, raising three issues. First, he challenges the sufficiency of the evidence, arguing that the evidence did not show a single conspiracy, as alleged in the indictment. Second, he argues that the district court abused its discretion in denying his motion for a new trial on the ground that the government's star witness, Joe Sharp, committed perjury. Third, Womack contends that the district court erred in imposing a sentence adding a firearm enhancement and finding that the amount of cocaine attributable to Womack was in excess of five kilograms. We affirm.

I. Conspiracy Variance
Womack first argues that the indictment charged a single, overarching conspiracy but the evidence failed to establish this single conspiracy. Instead, he argues, if the government proved anything, it proved the existence of multiple conspiracies, creating a variance.[1] A conspiracy variance claim is a challenge to the sufficiency of the evidence, which we review under a highly deferential standard. See United States v. Nitch, 477 F.3d 933, 936 (7th Cir.2007) (citing United States v. Townsend, 924 F.2d 1385, 1389 (7th Cir. 1991)); United States v. Williams, 272 F.3d 845, 862 (7th Cir.2001). Viewing the evidence in the light most favorable to the government, we ask whether the evidence is sufficient to support the jury's determination. United States v. Magana, 118 F.3d 1173, 1185 (7th Cir.1997).
To overturn a conspiracy conviction because of a variance, the defendant must show that there was a variance between what was charged in the indictment and the evidence at trial and that he was prejudiced by this variance. Williams, 272 F.3d at 862-63. Whether a single conspiracy exists is a question of fact for the jury. Townsend, 924 F.2d at 1389. "Even if the evidence arguably established the existence of multiple conspiracies, there is no material variance from the indictment charging a single conspiracy if a reasonable trier of fact could have found beyond a reasonable doubt the existence of the single conspiracy charged in the indictment." Williams, 272 F.3d at 862 (citing Townsend, 924 F.2d at 1389; United States v. McAllister, 29 F.3d 1180, 1186 (7th Cir.1994)).
Because Womack failed to ask for a jury instruction on multiple conspiracies or otherwise bring this challenge to the attention of the district court, we review that portion of Womack's conspiracy variance claim for plain error only. See United States v. Briscoe, 896 F.2d 1476, 1513 (7th Cir.1990) (applying plain error standard of review because defendants failed to propose multiple conspiracy jury instruction). To establish plain error, Womack must prove (1) that an error occurred; (2) that the error was plain; and (3) that the error affected his substantial rights. See Johnson v. United States, 520 U.S. 461, 117 S.Ct. 1544, 137 L.Ed.2d 718 (1997).
At trial, the government had the burden of proving the existence of a single conspiracy to distribute cocaine and that Womack knowingly became a member of the conspiracy with the intention to further the conspiracy.
The testimony established that Turner, a co-leader with Carl Parker of the cocaine-distribution ring, supplied Womack and Kareem Hamilton with multiple kilograms of cocaine, which Womack *795 and Hamilton then sold to others. Joe Sharp, who pleaded guilty to conspiring with Womack and others, testified that he acted as the courier, delivering cocaine concealed in dog food bags on at least ten occasions from Turner to Womack between May 2004 and January 2005. He further testified that he delivered kilogram-quantities to Womack. Sharp received $50 from Womack for each delivery. Sharp also testified that, at Turner's direction, he delivered two kilograms of cocaine from Womack to Hamilton. Consistent with Sharp's testimony, Hamilton testified that this delivery occurred around Christmas of 2004. Sharp also identified the speakers in various taped telephone conversations. In one conversation, Turner directed Womack on how to package the cocaine and then told Sharp to pick the cocaine up from Womack and deliver it to Hamilton. In a different conversation between Womack and Turner, Sharp's voice can be heard informing Womack that he, Womack, did not have to report to Turner and that he, Sharp, would contact Turner to report that he had picked up the packages for delivery. According to Sharp, it was standard procedure for him to call Turner to let him know that the cocaine had been picked up or delivered.
Anthony Watts, who pleaded guilty to conspiring with Womack and others, testified that he purchased four and a half ounces of cocaine from Womack in the summer of 2003. The cocaine that he had purchased was in chunks, indicating that it had been broken directly from a kilogram of cocaine, and was supplied to Womack by Turner. In 2004, Watts paid Womack $25,000 for a kilogram of cocaine. Later, Watts tried to buy another kilogram of cocaine from Womack but was unsuccessful; Womack could not reach Turner to get the cocaine.
Andre Denton also testified that Womack had told him that Turner was his source for cocaine. Corey Neal testified that Joe Sharp was a "runner" for Turner and that Sharp would often show up at Womack's home with a sack in his hand and then leave. Taken together, this testimony established the existence of a conspiracy among Turner, Womack, Hamilton, Sharp, and Watts to possess with intent to distribute cocaine in excess of five kilograms.
Womack argues that evidence also showed that Turner, Sharp, and Hamilton could have been involved in their own separate conspiracy and that Womack had separate dealings with Watts, Brian Greer, Denton, Anthony Stokes, and Neal. He argues further that there was no evidence that any of the cocaine delivered by Sharp ended up in the hands of Watts, Greer, Denton, Stokes, or Neal and that there was no evidence to tie all of these people into one solitary conspiracy. However, "[t]o join a conspiracy . . . is to join an agreement, rather than a group." Townsend, 924 F.2d at 1390. An on-going conspiracy exists even when individuals are coming and going without knowing the extent of the involvement of the other members or even knowing one another. The government was not required to show that Womack conspired with all of the previously indicted co-conspirators, that he was acquainted with Hamilton, Greer, Denton, Stokes, or Neal, or that they were acquainted with each other. The government needed only to prove that Womack joined the agreement alleged. Id. at 1389. On the evidence presented at trial, a reasonable jury could have found beyond a reasonable doubt that there was a single conspiracy to possess with intent to distribute cocaine in excess of five kilograms, in which Womack participated knowingly.


*796 II. Motion for a New Trial
Womack next argues that the district court abused its discretion in denying his motion for a new trial based on newly discovered evidence: Joe Sharp's perjured testimony.
Following his testimony and the conclusion of all evidence on April 4, 2006, Sharp was required to submit a urine sample for a drug test by the probation office. The test results showed a presumptive positive for marijuana. Sharp admitted to smoking marijuana on March 25, 2006 and signed a written statement to that effect. Neither the government nor Womack learned of Sharp's positive drug test until after the jury rendered its verdict. Eventually, Womack moved for a new trial based on newly discovered evidence, arguing that Sharp had perjured himself when testifying at Womack's trial by stating that he was not using drugs.[2] After a hearing, the district court denied Womack's motion for a new trial, finding that Womack had not established that a misrepresentation had occurred and that evidence that Sharp had used marijuana recently was cumulative and immaterial.
More specifically, the district court explained that the question posed to Sharp about "not using any other narcotic drugs or anything like that" was ambiguous as to the time frame and that Sharp could have interpreted the question to mean that very day. The district court also explained that Sharp may not have considered marijuana to be a "narcotic drug" since his prior addiction was to cocaine. Thus, Womack had failed to show that a misrepresentation had occurred. The district court reasoned further that since the jury also had heard that Sharp had been addicted to cocaine and that he had used drugs, evidence that Sharp had used marijuana recently was cumulative and, accordingly, immaterial. The district court then stated that there was no evidence that Sharp had used marijuana on the date that he testified and that Sharp's testimony was unaffected by any marijuana use. The district court also found that Sharp was a credible witness and that it would not have made a difference to the jury had they known that Sharp had made a misrepresentation about smoking marijuana or that he had smoked marijuana because he was otherwise so credible.
To win a new trial based on a claim that a government witness committed perjury (assuming as in this case that the government did not knowingly present the false testimony), Womack "will have to show that the existence of the perjured testimony (1) came to [his] knowledge only after trial; (2) could not have been discovered sooner with due diligence; (3) was material; and (4) would probably have led to an acquittal had it not been heard by the jury." United States v. Mitrione, 357 F.3d 712, 718 (7th Cir.2004), rev'd in part on Booker grounds, 543 U.S. 1097, 125 S.Ct. 984, 160 L.Ed.2d 988 (2005). Womack has failed to establish the requisite grounds for a new trial.
*797 In Jarrett v. United States, 822 F.2d 1438, 1445 (7th Cir.1987), a case virtually indistinguishable from the present one, the government's witness testified falsely as to her use of drugs on the day she testified against the defendant. After trial and the defendant's conviction, it was discovered that the witness had snorted THC on the day that she gave her testimony. This Court affirmed the district court's decision denying the defendant's motion for a new trial, reasoning that the jury had heard of the witness's history of drug use, and the judge and jury had ample opportunity to assess the witness's credibility. There also was no evidence in the record to establish that the witness had testified falsely regarding the defendant's participation in the robbery.
Jarrett is directly applicable here. Given the ambiguities in the questions posed to Sharp about his drug use, we agree with the district court's finding that Womack did not establish that Sharp had perjured himself. Even assuming that Sharp gave perjured testimony, however, his drug use was only relevant as to his ability "to perceive the underlying events and testify lucidly at trial." Id. at 1445 (citing United States v. Leonard, 494 F.2d 955, 971 (D.C.Cir.1974)). There was no indication that Sharp's testimony was impaired by his use of marijuana several days earlier or that it adversely affected his perception of the events in question. As in Jarrett, Womack's newly discovered evidence of Sharp's drug use was nothing more than "a collateral attempt to impeach" Sharp's testimony and was "therefore merely cumulative with respect to the question of [Sharp's] credibility concerning [his] use of drugs." Id. at 1446. Additionally, while Sharp admitted at trial that he was a drug courier and that he had used cocaine for years, the jury apparently found him credible as a witness. As a result, it is unlikely that the additional knowledge that Sharp had used marijuana recently would have influenced the jury to discredit Sharp's detailed testimony about the drug conspiracy. Thus, the district court properly denied Womack's motion for a new trial.

III. Womack's Sentence
Finally, Womack argues that the district court erred in enhancing his sentence for possession of a firearm and finding Womack's relevant conduct to include between five and fifteen kilograms of cocaine. Our review of the district court's factual findings at sentencing is for clear error; and our review of the application of those facts to the Sentencing Guidelines is de novo. United States v. Haddad, 462 F.3d 783, 793 (7th Cir.2006).
At the time of his arrest, Womack informed the arresting officers that he had a gun in his bedroom closet. At Womack's direction, the officers recovered a .40 caliber semiautomatic pistol, which was on the top shelf of the closet under some clothing, and $16,830 in cash, bundled in various denominations, from Womack's nightstand. After hearing the testimony at trial that Womack had a surveillance system at his home, that Sharp delivered cocaine to Womack at his home, and that Womack sold cocaine to Neal from his home, the district court inferred that the $16,830 was drug money and that the gun was connected to the cocaine trafficking. The district court therefore applied a two-level enhancement to Womack's offense level, pursuant to U.S.S.G. § 2D1.1(b)(1). We find that the district court did not clearly err in doing so.
"To support an enhancement under § 2D1.1(b)(1), the government bears the burden of proving by a preponderance of the evidence that a gun was possessed during the commission of the offense or relevant conduct." United States v. Olson, *798 450 F.3d 655, 684 (7th Cir.2006) (citing United States v. Berthiaume, 233 F.3d 1000, 1003-04 (7th Cir.2000)). "If the government satisfies this standard, the burden shifts to the defendant to show that it was clearly improbable that the gun was connected to the offense." Id. The government satisfied its burden with evidence that Womack had a gun in his possession at his home, where he received and sold cocaine, particularly when the gun was in such close proximity to a significant stash of money bundled in various denominations. Womack offered no contrary evidence. Thus, the district court did not err in adding the two-level enhancement to Womack's offense level for possession of a gun under § 2D1.1(b)(1).
The district court also did not err in finding that Womack's relevant conduct included between five and fifteen kilograms of cocaine. The jury rendered a special verdict finding that Womack conspired to distribute in excess of five kilograms of cocaine. On Sharp's testimony alone, who testified that he made ten or more deliveries of cocaine to Womack and that he delivered kilogram-quantities to Womack, the jury and the district court could reach the reasonable conclusion that Womack's relevant conduct included more than five kilograms of cocaine.
Moreover, the jury and the district court heard from Brian Greer, Anthony Watts, Andre Denton, and Corey Neal, who testified regarding the drugs that they had purchased or saw being purchased from Womack. Greer testified that he had bought four and a half ounces of cocaine from Womack at Womack's house in November or December 2003. In January or February 2004, he purchased an additional nine ounces of cocaine from Womack. Watts testified that he had purchased four and a half ounces of cocaine from Womack during the summer of 2003 and, during 2004, a kilogram of cocaine. Denton testified that he had witnessed Womack selling cocaine to "Chubbs" and Bacardi Holmes that was packaged in plastic sandwich bags. Neal testified that he did odd jobs for Womack and was paid between five and ten times with a gram or one-sixteenth of an ounce of cocaine. Neal also purchased a quarter-ounce of cocaine from Womack in the fall of 2004 and saw Womack selling an ounce of cocaine each to three individuals. Womack has not identified anything in the record that would lead to the conclusion that testimony of the government witnesses was unbelievable. Accordingly, we find that the district court did not clearly err in finding for purposes of sentencing that Womack's relevant conduct included between five and fifteen kilograms of cocaine.

IV. Conclusion
For the foregoing reasons, Womack's conviction and sentence are AFFIRMED.
NOTES
[1]  A variance occurs when the facts proved at trial differ from those charged in the indictment. See generally United States v. Miller, 471 U.S. 130, 105 S.Ct. 1811, 85 L.Ed.2d 99 (1985).
[2]  On direct examination, Sharp testified as follows:

Q. Getting out of time sequence just a little bit, was there a time you got yourself off of cocaine?
A. Yes, sir, it is.
Q. And about when would that have been?
A. At the turn of the millennium.
Q. Some time around 2000?
A. Yes.
On cross-examination by defense counsel, Sharp testified as follows:
Q. Now, you've stated that you got clean in about the year 2000, right?
A. Yes, sir, I did.
Q. And you're not using any other narcotic drugs or anything like that?
A. No, sir, I'm not.
