The correct answer is C and E
A: The first claim is untrue. The total number of options for selecting 4 out of 5 members is stated in the question's body. There are 5 completely unrestricted methods.
B: is untrue. There are four options for creating the committee if A must be on it. B, C, D, and E are each removed from the committee in turn.
C: This is true if members A and C are both on the committee. The three methods are ABCD, ACDE, and ACBE.
D: The solution is the same as the solution for Choice B if E must be on it. This claim is untrue.
E: The query is unclear. How many options are available to you? The answer is correct if you're picking a committee of just four people. I'll go ahead and assume that's what was intended, but the ambiguity can only be resolved by the asker.
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