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Risk committee composition

CombinatoricsMedium

A risk committee of $4$ people is chosen uniformly from $6$ quants and $5$ traders, all distinct people. How many committees contain at least $2$ traders?

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Hint

Count the complement: committees with too few traders.

Solution

The total number of committees is $(4 11) = 330$ .
Committees with $0$ traders: $(4 6) = 15$ .
Committees with exactly $1$ trader: $5 \times (3 6) = 5 \times 20 = 100$ .
Subtract the bad cases: $330 - 15 - 100$ .
Therefore the answer is $215$ .

Answer: $215$

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