In a community chorus, 10 people are candidates for the board of directors. The board has 6 members: 4 officers (president, vice president, secretary, and treasurer) and 2 at-large members (who don’t have an office.

Question

First, the four officers are chosen. In how many ways can 4 of the 10 candidates be chosen?

Answer 1

The number of ways to choose 4 officers from a pool of 10 candidates is given by the combination "10 choose 4," which is calculated as:

10 choose 4 = 10! / (4! * (10-4)!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 10 * 3 * 7 = 210.

Therefore, there are 210 ways to choose 4 officers from the 10 candidates.