Suppose I must form a committee of 3 people chosen out of 7. 2 of the 7 are enemies of each other. These 2 people would wreak havoc if they are both chosen to be on the committee. How may ways are there to form committees containing both of them?
Why is the answer $\binom{2}{2}\binom{5}{1} = 5$? Why am I picking 2 out of 2 people and then 1 out of 5 people?