# Combinations: 5 seniors, 3 juniors to form committee of 5.

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?)

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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