In how many ways can a group of 5 men and 2 women be formed from 7 men and 3 women?

Problem restatementSelect 5 men from 7 and 2 women from 3; multiply independent choices.

Given data

• Men available = 7; choose 5.
• Women available = 3; choose 2.

Concept/ApproachUse combinations; choices are independent.

Step-by-step calculation Ways to choose men = C(7, 5) = 21 Ways to choose women = C(3, 2) = 3 Total groups = 21 × 3 = 63

Verification/AlternativeEquivalently, choose the two excluded men (C(7,2)=21) and the one excluded woman (C(3,1)=3) → same result.

Final Answer63