Question

a firm wants to select a group of 8 out of its 20 employees to attend a Business trip .in how many ways can this be done if there is a couple who must not be separated​

Answer 1

Case 1 - 50388 ways when the couple is there in the group of 8 people selected out of 20 employees.

Case 2 - 75582 ways when the couple is not there in the group of 8 people selected out of 20 employees.

Explanation:

Given

The couple within the group can not be separated and hence instead of taking total 20 employees , it must be taken as 19 employees.

Now if the couple is there in the selected group of 8 people, then total 7 needs to be selected out of 19 and hence the total number of ways of selecting 7 people out of 19 is

`^7C_(19)` = 50388

If the couple is not there in the selected group of 8 people, then the total number of ways of selecting 8 people out of 19 is

`^8C_(19)` = 75582