Compute Probabilities Involving Permutations and Combinations
-A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 8 members and any member can be elected to each position No person can hold more than one office.
A) 336
B) 168
C) 112
D) 1680

Question

Quizplus · Accepted Answer

Since no person can hold more than one office and there are 3 positions to fill from 8 members, we use permutations because the order matters (different positions). The formula for permutations is P(n, r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to choose. Here, n = 8 (members) and r = 3 (positions), so P(8, 3) = 8! / (8-3)! = 8! / 5! = (8×7×6×5!) / 5! = 8×7×6 = 336.