Simple committee count: From a group of 6 men and 4 women, how many 4-person committees can be formed (no constraints)?

Introduction / Context:With no restrictions, the number of committees depends only on total group size and committee size. Gender labels do not matter for counting unless constraints are imposed.

Given Data / Assumptions:Total people = 10; committee size = 4.

Concept / Approach:Use combinations C(10, 4) since order of selection does not matter.

Step-by-Step Solution:

Verification / Alternative check:Symmetry: C(10, 4) = C(10, 6) = 210.

Why Other Options Are Wrong:225, 195, 185 do not equal C(10, 4).

Common Pitfalls:Using permutations instead of combinations.

Final Answer:210