In how many ways can a committee of 5 men and 6 women be formed from 8 men and 10 women?

Problem restatementSelect 5 men and 6 women independently from their respective pools.

Given data

• Men available = 8; choose 5.
• Women available = 10; choose 6.

Concept/ApproachUse combinations and multiply independent choices.

Step-by-step calculation Ways to choose men = C(8, 5) = 56 Ways to choose women = C(10, 6) = 210 Total committees = 56 × 210 = 11760

Verification/AlternativeBy symmetry, C(10, 6) = C(10, 4) = 210; the product remains 11760.

Final Answer11760