📐 Mathematics · Permutations and Combinations · JEE

From 6 men and 4 women, the number of 5-member committees with at least 2 women is:

Answer: 186.

Correct answer: C. 186

Explanation: Total C(10,5) = 252, minus 0 women C(6,5) = 6 and exactly 1 woman C(4,1)C(6,4) = 60. So 252 − 66 = 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