A committee of four is formed from five eligible members. Let the eligible members be represented with A, B, C, D, and E. The possible outcomes include S = {ABCD, BCDE, ACDE, ABCE, ABDE}. Which statements about the situation are true? Check all that apply.

A. There are 120 different ways to choose the committee.
B. If person A must be on the committee, there is only one way to form the committee.
C. If persons A and C must be on the committee, there are three ways to form the committee.
D. There are five ways to form the committee if person E must be on it.
E. If the number of eligible members increases, the number of outcomes increases