Question

A committee is to be formed with a president, a vice president, and a treasurer. If there are 10 people to select from, how many committees are possible?

Answer 1

This is a classic permutation problem.

We are given the number of permutations of 10 things taken 3 at a

time. Note: ORDER MATTERS because President, Vice-President,

and Treasurer are ordered by rank.

The needed formula is

P(n, r) = n!/(n - r)!

P(10, 3) = 10!/(10 - 3)!

P(10, 3) = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(7 x 6 x 5 x 4 x 3 x 2 x 1)

We cancel out 7 factorial down to 1 factorial on the top and bottom.

This leaves us with 10 x 8 x 9.

P(10, 3) = 10 x 9 x 8

P(10, 3) = 90 x 8

P(10, 3) = 720

Answer: 720 committees are possible.

Did you follow? This is a probability question regarding permutation.