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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?


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$.


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

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Yes, the answer should be correct – malin Nov 3 '12 at 13:34
(and this kind of question is OK.) – M.B. Nov 3 '12 at 13:34
Thanks. Good to know its allowed. Didn't want to ask without posting an attempt. I suppose I'll answer my question with "yes my reasoning is correct"? – Legendre Nov 3 '12 at 13:38
Sure and accept your answer. – M.B. Nov 3 '12 at 14:27
The thing to remember is the more constraint you have on a choice to make, the more you want to make that choice first – Jean-Sébastien Nov 3 '12 at 14:30
up vote 1 down vote accepted

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. $$\binom{5}{3}\binom{3}{3}\binom{2}{2} + \binom{5}{4}\binom{4}{3}\binom{2}{1} + \binom{5}{5}\binom{5}{3}\binom{2}{0}$$ – N. F. Taussig Apr 10 at 12:19

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