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Combinatorics-N boys and M girls are learning acting skills from a theatre in Mumbai.

N boys and M girls are learning acting skills from a theatre. To perform a play they need to form a group of P actors containing not less than 4 boys and not less than 1 girl. The theatre requires you to write a program that tells them the number of ways the group can be formed.

Note: Composition should be unique and not the order in which the composition is made of.

I have tried a lot but can't get over some of my confusions. How can i solve this ?

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    You should tell us what "your confusions" are...2012-02-23
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    @ Arturo Magidin I was considering a case of 6 boys and 2 girls. Now i started with _6C4 * 2C1 + 6C5 * 2C2 + 6C6 * ? ._ Now i can substitute 2C1 or 2C2 in place of ? . Do i have to consider this case for each case ?2012-02-23
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    (1) You are saying what $N$ and $M$ is, but you don't say what $P$ is; without $P$, you aren't calculating anything. (2) What is it your summands are supposed to be counting? The first summand seems to be that you are selecting four boys and one girl (so your $P$ would be 5); but the next summand suggests you are selecting 5 boys and 2 girls (now your cast is 7?).2012-02-23
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    @ Arturo Magidin P is the total number of actors in a play. They could vary to satisfy the condition of _atleast_.2012-02-23
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    @steve: I am aware what $P$ is. My point is that if you want to solve the problem with specific numbers, it is not enough to specify how many boys and how many girls there are, you **also** need to specify what $P$ is. Otherwise, your answer needs to have $P$s all over the place. That's why your attempted answer is nonsense: without a specific $P$, or without leaving $P$ indicated, whatever it is you think you are counting has nothing whatsoever to do with the problem at hand.2012-02-23

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