Brent’s after-school game club has 12 members from which a six-member team is created. Miguel’s after-school sports club has 10 members from which a six-member team is created. Which student’s club has more possible combinations for his six-member team?

The number of six-member teams is found by choosing 6 members from each club, without regard to order. Brent’s club has 12 members, giving 12 choose 6 = 924 possible teams; Miguel’s club has 10 members, giving 10 choose 6 = 210. Brent’s club has more possible combinations because there are more members to choose from.

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