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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 85

From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is :

Choose one option
Answer and worked solution

Official answer: C

Committees with at least one woman: (154)−(104)=1155\binom{15}4-\binom{10}4=1155. More women than men: (53)(101)+(54)=105\binom53\binom{10}1+\binom54=105. The probability is 1051155=111\frac{105}{1155}=\frac1{11}.

Topics:Classical probabilityCombinations
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