Ben needs to form a committee of 3 from a group of 8 engineers. If two of the engineers cannot serve together, how many different committees can Ben form?
Assume A and B are these two gentlemen in question.
Total ways of selecting engineers = C(8,3) = 56.
1. A included.
2. B included.
3. A and B included.
4. Nither A or B included.
Of course we need to discard the case of A and B included which is
C(6, 1) = 6.
Therefore, remaining cases, when these two gentlemen don't serve together = 56 - 6 = 50.
Who says elephants can't dance?