Question

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man

Answer 1

70 possible groups

Explanation:

Given the total number of employee to be equal to 12 temporary employee.

Number of women employee = 5 women

Number of men employee = 12 - 5 = 7 men

If 4 will be hired as permanent employees, the possible ways they can be grouped so that the 4 temporary employees consists of 3 women and 1 man can be done by applying the combination formula.

Combination has to do with selection. For example, if r objects are to be selected from n pool of similar objects, this can be done in nCr different ways.

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

According to question, we are to select 3 women from 5 women and 1 man from 7 men. Based on similarity in sex, this can be done in (5C3* 7C1) different ways .

`5C3 * 7C1\\= (5!)/((5-3)!3!) * (7!)/((7-1)!1!)\\\\= (5!)/(2!3!) * (7!)/(6!1!)\\\\= (5*4*3!)/(3!*2) * (7*6!)/(6!*1)\\\\= (20)/(2) * (7)/(1)\\ \\= 10*7\\\\= 70\ possible\ groups`