Question

JCL Computers has five vacancies in its executive trainee program. In how many ways can the company select five trainees from a group of twelve female and twelve male applicants if the vacancies

(a) Can be filled by any combination of men and women?

ways?

(b) Must be filled by two men and three women?

ways?

Answer 1

Combinations represent the selection of some or all of different objects in which order of selection doesn’t matter.

The number of combinations is the number of ways in which we can select a group of objects from a set.

a) We are to select 5 employees from 12+12=24 persons where order doesn't matter. Since it can be filled with any combination, it is just selection of any 5 out of total 24 candidates; this is given by =24!/(5!*19!) =42504
b) While selecting 5 people we must have 2 men and 3 women which can be done by taking 2 men from 12men in ways and 3 women from 12 women in ways.

The total number of ways to do it

=14520