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NDA 2019 Maths · Mathematics · Permutations and Combinations · medium

A committee of 4 is to be chosen from 6 men and 4 women so that it has at least 2 women.

Single correct option

A committee of 44 is to be chosen from 66 men and 44 women so that it has at least 22 women. The number of ways is
  1. A. 9090
  2. B. 115115
  3. C. 114114
  4. D. 210210
Show answer and solution

Answer: (B) 115115

Add the cases: 22 women (42)(62)=90\binom42\binom62=90, 33 women (43)(61)=24\binom43\binom61=24, 44 women 11. Total 115115. Option 9090 counts only the exactly-two-women case; 210210 ignores the condition.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake