[JEE Advanced 1994] a committee of 12 from 9 women and 8 men with at least 5
A committee of $12$ from $9$ women and $8$ men with at least $5$ women. Find the total; also (a) women in majority, (b) men in majority.
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· 2d ago
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Answer: Total $6062$; (a) women-majority $2702$; (b) men-majority $1008$.
Summing $\binom9w\binom8{12-w}$ for $w=5,\dots,9$ gives $1008+2352+2016+630+56=6062$. Women majority ($w\ge7$): $2016+630+56=2702$; men majority ($w=5$): $1008$.
JEE Advanced 1994 · Permutations and Combinations — verified solution by the Vidaara Team.
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