Out of 4 men and 4 women, how many different committees of exactly 3 men and 2 women can be formed (order does not matter)?

Introduction / Context:We select fixed counts from each subgroup. Order of members on a committee is irrelevant, so use combinations.

Given Data / Assumptions:

• Men = 4; choose 3.
• Women = 4; choose 2.
• Committees are sets (no roles or ordering).

Concept / Approach:Compute C(4,3) * C(4,2) by independence across disjoint groups.

Step-by-Step Solution:C(4,3) = 4.C(4,2) = 6.Total = 4 * 6 = 24.

Verification / Alternative check:Enumerating men first, then women, or vice versa, yields the same product.

Why Other Options Are Wrong:20 and 16 are near-miss counts (e.g., forgetting some combinations); 15 is C(6,2) and unrelated.

Common Pitfalls:Accidentally using permutations or mixing order into a committee selection.

Final Answer:24