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There are $5$ senior students and $3$ junior students. They are to form a committee of $5$, in which $3$ are decision makers and $2$ handle logistics. Only seniors can be decision makers. But anyone can handle the logistics.

How many possible combinations (order does not matter within the two designations) are there?

Attempt

Out of $5$ seniors, we choose $3$ to be decision makers. Then, in the remaining $5$ students, we choose $2$ to handle logistics. Thus, the answer is: $5 \choose 3$$5 \choose 2$.

Question

Is my reasoning correct? (is this kind of question allowed here?)

  • 0
    @MarcvanLeeuwen - Yes the role matters.2012-11-04

1 Answers 1

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Based on the comments, my reasoning is correct.

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    Your answer is incorrect. We must select how many seniors are on the committee, which seniors occupy decision-making positions, and which juniors are on the committee. $\binom{5}{3}\binom{3}{3}\binom{2}{2} + \binom{5}{4}\binom{4}{3}\binom{2}{1} + \binom{5}{5}\binom{5}{3}\binom{2}{0}$2016-04-10