Question

There are 5 positions open. 20 candidates applied. 14 are men, 6 are women. The

company decided to give 3 positions to men, 2 to women. How many outcomes are
possible?

Answer 1

2307 ways

Explanation:

Given

Candidates: 5

Men (Applicants): 14

Women (Applicants): 6

Job Positions: 5

Man = 3

Women = 2

Required:

Number of possible outcomes

This question represent selection; i.e. selecting candidates for job positions;

This question can be solved by using Permutations/Selection formula

Given that 3 man are to be selected from 14 men and 2 women from a total of 6 women

Let M represent Men and W represent Woman

Number of ways = M + W

Calculating M

`M = nPr`

Substitute nPr with its formular

`M = (n!)/((n-r)!)`

Where n = 14 men and r = 3 applied

`M = (14!)/((14 - 3)!)`

`M = (14!)/(11!)`

`M = (14*13*12*11!)/(11!)`

`M = 14*13*12`

`M = 2184`

Calculating W

`W = nPr`

Substitute nPr with its formula

`W = (n!)/((n-r)!)`

Where n = 6 men and r = 2 applied

`W = (6!)/((6-2)!)`

`W = (6!)/(2!)`

`W = (6*5*4*3!)/(2!)`

`W = 6*5*4`

`W = 120`

Recall that Number of ways = M + W

Number of Ways = 2184 + 123

Number of Ways = 2307