First, you are dealing with combinations not permutations since this answer does not consider order (i.e., whether Michael is chosen before Anthony etc.)
So, the combination formula is n!/((n-k)!k!).
Then, you plug in the numbers and get the number of possible sub-committees. Then, you deal with the fact that you are only interested in a certain number of sub-committees (namely ones that include Michael and also include Anthony).
For more information on combinatorics, check out the following links:
Combinatorics (Wikipedia)
Combinatorics (Math World)
Combinatorics (GMAT Study Guide)
I hope this helps.