A department has 16 employees (8 men and 8 women). You must form a project team with exactly 3 men and 3 women. How many distinct teams are possible (order does not matter)?

Introduction / Context:This is a direct combinations problem: select a fixed count from each of two disjoint groups (men and women) where order is irrelevant and no role distinctions exist within a chosen team.

Given Data / Assumptions:

• Men = 8, Women = 8.
• Select exactly 3 men and exactly 3 women.
• Teams are sets; internal order does not matter.

Concept / Approach:Use combinations independently on each group and multiply: total ways = C(8,3) * C(8,3). This is the fundamental rule of counting for independent choices across disjoint sets.

Step-by-Step Solution:C(8,3) = 8*7*6 / (3*2*1) = 56.Total teams = 56 * 56 = 3136.

Verification / Alternative check:Symmetry implies selecting either gender first yields the same multiplication. No ordering or role labels are present, so there is no extra factorial factor.

Why Other Options Are Wrong:112 and 720 come from misusing permutations or partial counts; 112896 multiplies by spurious orderings.

Common Pitfalls:Accidentally using permutations (which would imply ordered roles) or adding instead of multiplying across independent gender selections.

Final Answer:3136