Topic Permutations and Combinations A club has 14 members a

Topic: Permutations and Combinations

A club has 14 members.

a) How many ways can a governing commitee of size 3 be chosen?

b) How many ways can a president, vice president, and treasurer be chosen?

c) How many ways can a president, vice president, and treasurer be chosen if two specified club members refuse to serve together?

Solution

a) ⁿC_r (14, 3) = 14! / [3! * (14-3)!] = 364

b) ⁿP_r (14, 3) = 14! / (14 -3)! = 2184

c)

Neither of the two: ⁿP_r (12, 3) = 12! / (12 -3)! = 1320

One of the two: ²C₁ * ⁿP_r (12, 2) = 2 * 12! / (12 -2)! = 792

Total = 1320 + 792 = 2112