From 8 men and 7 women (15 persons total), how many distinct groups of 6 persons can be formed? (Order within the group does not matter.)

Introduction / Context:We are forming groups (unordered selections). This is a direct application of combinations: the number of ways to pick k people from n distinct people is C(n, k).

Given Data / Assumptions:

• Total people = 8 + 7 = 15.
• Group size = 6.
• Order inside a group does not matter (pure selection).

Concept / Approach:Use C(n, k) = n! / (k! (n − k)!). Here n = 15 and k = 6.

Step-by-Step Solution:

Verification / Alternative check:Symmetry C(15, 6) = C(15, 9) holds; calculators or Pascal-style reasoning confirm 5005.

Why Other Options Are Wrong:5000 and 5050 are close but not exact; “None of these” is not needed because 5005 is precise.

Common Pitfalls:Accidentally treating it as permutations (ordering groups), which would overcount.

Final Answer:5005