📐 Mathematics · Permutations and Combinations · JEE

Number of ways to choose a committee of 5 from 10 where at least 2 women (4 women, 6 men):

Answer: 186.

A 186
B 180
C 210
D 252

Correct answer: A. 186

Explanation: Exactly 2 women: C(4,2)×C(6,3) = 6×20 = 120. Exactly 3 women: C(4,3)×C(6,2) = 4×15 = 60. Exactly 4 women: C(4,4)×C(6,1) = 1×6 = 6. Total = 120+60+6 = 186.

Counting tree for selecting 2 items from {A, B, C} without repetition: 3 x 2 = 6 ordered arrangements.

Concept context

Counting, arrangements, and selections

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Number of ways to choose a committee of 5 from 10 where at least 2 women (4 women, 6 men):

Concept context

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