In what follows, let C(n,k) denote the combination of n taking k.

1) C(20,4)*C(16,3), choose the math fair then the Math News from who is left.

2) C(20,4)*C(20,3), choose the math fair then the Math News from the same pool.

3) Is the difference: #2 - #1

4) C(20,2)*C(18,2)*C(16,1)= [20!]/([2!]^2[15!]).

Here another way to think about #4. Suppose we have 2 B's, 2 F's, 1 M & 15 X's. How many ways can we form a string of the letters? If a person in our list get a B, that person is in both; F means math fair; M means Math News; and X means not chosen.

CORRECTED! Thanks Soroban