There are 13 members on a board of directors. If they must form a subcommittee of 5 members, how many different subcommittees are possible?
A)120
B)1287
C)154,440
D)371,293

Question

Quizplus · Accepted Answer

The number of ways to choose a subcommittee of 5 members from a group of 13 is calculated using the combination formula, which is C(n, k) = n! / [k!(n - k)!], where n is the total number of items (13 members), k is the number of items to choose (5 members), and "!" denotes factorial. Thus, C(13, 5) = 13! / [5!(13 - 5)!] = 13! / (5!8!) = (13×12×11×10×9) / (5×4×3×2×1) = 1287.

There Are 13 Members on a Board of Directors