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?

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

Substitute nPr with its formular

Where n = 14 men and r = 3 applied

Calculating W

Substitute nPr with its formula

Where n = 6 men and r = 2 applied

Recall that Number of ways = M + W

Number of Ways = 2184 + 123

Number of Ways = 2307

there would only be 50 odd numbers between 1 and 100 so therefor there would be 50 even so that would only be 50 odd numbers.