Question

(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?

(B) How many ways can a president and vice-president be chosen from a committee of 8 people?

Answer 1

28, 56

56

Explanation:

a

To solve this, we use the combination rule.

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

n is the number of options (8) k is the number of slots (2).

Assuming the order doesn't matter, then

8C2 = 8! / 2!(8-2)!

8C2 = 8! / 2! 6!

8C2 = 40320 / 2 * 720

8C2 = 40320 / 1440

8C2 = 28

If the order does matter, then we use permutation instead.

nPk = n!/(n-k!) where n = 8 and k =2 8P2 = 8! / 6!

8P2 = 40320 / 720

8P2 = 56

b

We are told that there exist 8 ways to choose a president and a vice president. This means that, after choosing a president from 8 people, there remains 7 people to choose his vice from. Thus, the number of ways to choose a president and his vice are 8 * 7 = 56