Question

Exercise topic: Permutations and Combinations. A company wants to hire 3 new employees, but there are 8 candidates, 6 of them which are men and 2 are women. If the selection is random: a) In how many different ways can choose new employees? b) In how many different ways can choose a single male candidate? c) In how many different ways can choose at least one male candidate? with procedures. Help me please..

Answer 1

(a) 56 ways

(b) 6 ways

(c) 56 ways

Explanation:

Given:

candidates: 6 mail, 1 female

number to hire : 3

a) In how many different ways can choose new employees?

use the combination formula to choose r to hire out of n candidates

C(n,r) = C(8,3) = 8! / (3! (8-3)! ) = 40320 / (120*6) = 56 ways

b) In how many different ways can choose a single male candidate?

6 ways to choose a male, one way to choose two female, so 6*1 = 6 ways

c) In how many different ways can choose at least one male candidate?

To choose at least 1 male candidate, we subtract the ways to choose no male candidates out of 56.

Since there are only two females, there is no way to choose 3 female candidates.

In other words, there are 56-0 = 56 ways (as in part (a) ) to hire 3 employees with at least one male candidate.