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""Find a power series associated with the problem where we have to find a number of ways to select 10 people to form and expert committee from 6 Professors and 12 Associate Professors.""

Question stated in our college assigment but how to solve this ???

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Do you have any worked problems like it? Anything like it in your lecture notes? Textbook? – Gerry Myerson Sep 27 '12 at 1:07
@GerryMyerson ya but their is no clear answer or any hints for solving it – SaurabhLP Sep 27 '12 at 1:15
If your teacher has given you a problem to solve, and really hasn't done anything like it in lectures or in handouts or in the text, then you ought to go to your teacher and ask how you're supposed to do the problem. But first you had better be absolutely sure there isn't something very much like it in one of those resources. Maybe the best approach is to ask your teacher to point you to the exact place where you were given an example of a problem like this one. – Gerry Myerson Sep 27 '12 at 5:40

HINT: I can think of at other possibilities, but the most natural power series in this context would be

$$\sum_{n\ge 0}c_nx^n\;,$$

where $c_n$ is the number of ways to form an $n$-person committee from the group of $6$ professors and $12$ associate professors. Of course for $n>18$ we must have $c_n=0$, but what is $c_n$ when $0\le n\le 18$? Those are the coefficients that you want for your power series.

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Its correct but i need to have more explanation for that... – SaurabhLP Sep 27 '12 at 1:57
@SaurabhLP: Let’s try something more concrete first. Can you find $c_{10}$, the number of $10$-person committees that can be formed? – Brian M. Scott Sep 27 '12 at 2:00
do you mean let n=10 and then placing it in the given expression... – SaurabhLP Sep 27 '12 at 2:07
@SaurabhLP: No, I mean answering this question: How many $10$-person committees can be formed from a group consisting of $6$ professors and $12$ associate professors? – Brian M. Scott Sep 27 '12 at 2:09

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