Answer:
(a) 56 ways
(b) 6 ways
(c) 56 ways
Step-by-step 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.
