Question

Assume that 11 people, including the husband and wife pair, apply for 5 sales positions. People are hired at random. (1) what is the probability that both the husband and wife are hired

Answer 1

The probability that both the husband and wife are hired is
`(2)/(11)`

Step-by-step explanation

Total number of people = 11 and total number of sales positions = 5

So, the total possible number of ways for selecting 5 people from 11 people will be:
`^1^1C_(5)`

Now if both the husband and wife are hired, then it means the remaining (5-2)= 3 positions are filled from the remaining (11 -2) = 9 people.

So, the possible number of ways for selecting 3 people from 9 people will be:
`^9C_(3)`

Thus, the probability
`= (^9C_(3))/(^1^1C_(5))=(84)/(462)=(2)/(11)`