There are 8 employees including Bob and Rachel. If 2 employees are to be randomly chosen to form a committee.

Question

There are 8 employees including Bob and Rachel. If 2 employees are to be randomly chosen to form a committee, what is the probability that the committee includes both Bob and Rachel?

Jaideep Hooda · Answer

First, let's count the total number of 2 people committee from a 8 people pool. The answer is 8C2 i.e. 28. So there are 28 possible sets of 2 people committees.

Now, let's count the total number of ways Bob and Rachel are chosen together. That will be 1. (This is the key step. If this step is not evident, make up letters for remaining 6 employees, and list out all the possible 2 employee groups for the sake of understanding how we landed with 1)

Probability of Rachel and Bob being chosen = Number of ways Bob and Rachel are chosen/Total number of 2 people committees.

Therefore, Answer = 1/28.