A company's board of directors wants to form a committee of of its members. There are members to choose from. How many different committees of members could possibly be formed?

21

Explanation:

The question is incomplete, as it must provide the total number of directors and the maximum number of directors in one committee.

E. g. The question may be complete as, "A company's board of directors wants to form a committee of 2 of its members. There are 7 members to choose from. How many different committees of 2 members could possibly be formed?

From 7 members, 2 to be chosen at a time is found by

= 7! / (7-2) ! (2!)

= 7*6 / 2*1

= 21 ways