A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed?

Question

A 2-member executive committee is to be formed from a 12-member board of directors. In how many ways can it be formed? ​

Quizplus · Accepted Answer

We can use the combination formula to solve this problem:

nCk = n! / (k! * (n-k)!)

where n is the total number of people (12 directors) and k is the number of people we want to select (2 for the executive committee).

Plugging in the numbers, we get:

12C2 = 12! / (2! * (12-2)!) = 12! / (2! * 10!) = (12 * 11) / 2 = 66

Therefore, there are 66 ways to form a 2-member executive committee from a 12-member board of directors. The answer is choice C.

A 2-Member Executive Committee Is to Be Formed from a 12-Member