Answer:
Step-by-step 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.
[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]
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 .
[tex]5C3 * 7C1\\= \frac{5!}{(5-3)!3!} * \frac{7!}{(7-1)!1!}\\\\= \frac{5!}{2!3!} * \frac{7!}{6!1!}\\\\= \frac{5*4*3!}{3!*2} * \frac{7*6!}{6!*1}\\\\= \frac{20}{2} * \frac{7}{1}\\ \\= 10*7\\\\= 70\ possible\ groups[/tex]
