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 $\frac{2}{11}$

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 $= \frac{^9C_{3}}{^1^1C_{5}}=\frac{84}{462}=\frac{2}{11}$