Question

There are 6 women and 5 men interviewing for 4 cashier positions at Walmart. In how many ways can the positions be filled if 2 women and 2 men are hired?

Answer 1

Answer:

The positions can be filled in 150 ways.

Step-by-step explanation:

The order in which the people are chosen is not important. For example, A, B, C, D is the same outcome as B, A, C, D. So we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

In how many ways can the positions be filled if 2 women and 2 men are hired?

2 women from a set of 6.

2 men from a set of 5.

So

$T = C_{6,2} \times C_{5,2} = \frac{6!}{2!(6-2)!} \times \frac{5!}{2!(5-2)!} = 120$

The positions can be filled in 150 ways.

Answer 2

The number of ways the position can be filled with 2 women and 2 mean is 150

The number of people is:

$\mathbf{Women = 6}$

$\mathbf{Men = 5}$

The number of selection is:

$\mathbf{Women = 2}$

$\mathbf{Men = 2}$

So, the number of ways of selection is calculated using:

$\mathbf{Ways = ^nC_r}$

This gives

$\mathbf{Ways = ^6C_2 \times ^5C_2}$

Apply combination formula

$\mathbf{Ways =15 \times 10}$

$\mathbf{Ways =150}$

Hence, the number of ways the position can be filled with 2 women and 2 mean is 150

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