Question

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible

Answer 1

Answer: 80

Explanation:

Given : Number of married couples = 5

Number of people required = 3

Since , the committee does not include two people who are married to each other,

We consider 1 married couple as one people , then the number of ways to select 3 persons =
`^(5)C_3=(5!)/(3!(5-3)!)=(5*4*3!)/(3!*2)=10`

Also, chances of selecting any partner = 2 (either Husband or wife)

So for 3 persons the total chances =(2) (2) (2)

Total number of ways to form the committee so that the committee does not include two people who are married to each other= 10 x (2) (2) (2) =80

Hence, the number of committees are possible = 80