Question

1) From 8 names on a ballot, a committee of 3 will be elected to attend a political national convention How many different committees are possible?

A) permutations

B) combinations

Answer 1

Answer:

a) 336 different committees are possible.

b) 56 different committees are possible.

Step-by-step explanation:

Permutations:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Combinations:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

In this question:

$n = 8, x = 3$

A) permutations

$P_{(8,3)} = \frac{8!}{(8-3)!} = 336$

336 different committees are possible.

B) combinations

$C_{8,3} = \frac{8!}{3!(8-3)!} = 56$

56 different committees are possible.