I have two committees A and B, with |A| = 3 = |B|, out of a group of 8
people such that at most one person can serve on both committees. How many ways we can form the committees A and B? Please show me how it's done.
In this question, we need to consider two cases. Notice that the question says that "at most" one person can serve on both committees. This means that there could be zero or one person on both committee. We need to separate the two cases and consider them differently.
(1) For the case that no person serves on both committee
Then the selection process is as follows: we would first select three people ...
This provides an example of determining the number of ways specific groups can be formed.