Forming a committee from men and women: In how many ways can a committee of 3 men and 3 women be formed from 6 men and 5 women?

Introduction / Context:We independently choose required counts from men and women, then multiply by the multiplication principle because selections are independent categories (men vs women). Order within the committee does not matter (combinations, not permutations).

Given Data / Assumptions:

• Men: choose 3 from 6 → C(6,3).
• Women: choose 3 from 5 → C(5,3).
• Total committees = product of these combinations.

Concept / Approach:

• Use combinations because only membership matters.
• Multiply independent category choices.

Step-by-Step Solution:

Verification / Alternative check:Enumerating by first choosing all 6 and then picking which 3 are men also reduces to the same product once symmetry is accounted for; 200 is exact.

Why Other Options Are Wrong:

• 180, 150, 210 are common distractors from misapplying permutations or adding counts.

Common Pitfalls:

• Using permutations (ordering), which would overcount identical committees.

Final Answer:200