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NeX [460]
3 years ago
14

Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees a

re women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man
Mathematics
1 answer:
Ivenika [448]3 years ago
8 0

Answer:

<h2>70 possible groups</h2>

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 <em>nCr </em>different ways.

nCr = \frac{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\\=  \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

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