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

Answer:

2307 ways

Step-by-step 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

$M = \frac{n!}{(n-r)!}$

Where n = 14 men and r = 3 applied

$M = \frac{14!}{(14 - 3)!}$

$M = \frac{14!}{11!}$

$M = \frac{14*13*12*11!}{11!}$

$M = 14*13*12$

$M = 2184$

Calculating W

$W = nPr$

Substitute nPr with its formula

$W = \frac{n!}{(n-r)!}$

Where n = 6 men and r = 2 applied

$W = \frac{6!}{(6-2)!}$

$W = \frac{6!}{2!}$

$W = \frac{6*5*4*3!}{2!}$

$W = 6*5*4$

$W = 120$

Recall that Number of ways = M + W

Number of Ways = 2184 + 123

Number of Ways = 2307