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JEE Main 2016 · Mathematics · Permutations and Combinations · medium

From a group of 6 men and 4 women, a four-member team containing at least two women is to be formed. In how many ways can this be done?

Single correct option

From a group of 66 men and 44 women, a four-member team containing at least two women is to be formed. In how many ways can this be done?
  1. A. 9090
  2. B. 185185
  3. C. 210210
  4. D. 115115
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Answer: (D) 115115

Cases: 2 women (42)(62)=6⋅15=90\binom42\binom62=6\cdot15=90; 3 women (43)(61)=24\binom43\binom61=24; 4 women (44)=1\binom44=1. Total =90+24+1=115=90+24+1=115. (Complement check: (104)−(64)−(41)(63)=210−15−80=115\binom{10}{4}-\binom64-\binom41\binom63=210-15-80=115.)
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Original question written in the JEE Main 2016 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake