Question

From the 6 male and 11 female salesrepresentatives for an insurancecompany, a team of 4 men and 2women will be selected to attend anational conference on insurancefraud.

Answer 1

`825\text{ ways}`

Step-by-step explanation:

Here, we want to get the number of ways in which the team of 6 will be selected

From the question, out of 6 males, 4 will be selected, while out of 11 females, 2 will be selected

To select r from a total of n, we use the following formula:

`^nC_r\text{ = }(n!)/((n-r)!r!)`

Selecting 4 out of 6, we have:

`^6C_4\text{ = }(6!)/((6-4)!4!)\text{ = 15}`

For the second part, we are selecting 2 out of 11, we have that as:

`^(11)C_2\text{ = }(11!)/((11-2)!2!)\text{ = 55}`

The total number of ways will be the product of the two as follows:

`55*15\text{ = 825 ways}`