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

a) 336 different committees are possible.

b) 56 different committees are possible.

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) = (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)) = (n!)/((n-x)!)`

In this question:

`n = 8, x = 3`

A) permutations

`P_((8,3)) = (8!)/((8-3)!) = 336`

336 different committees are possible.

B) combinations

`C_(8,3) = (8!)/(3!(8-3)!) = 56`

56 different committees are possible.