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N boys and M girls are learning acting skills from a theatre in Mumbai. To perform a play on ‘Ramayana’ 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.

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    **Hint**: I think you can reduce this problem by assuming $4$ of the $P$ slots are filled by boys, and $1$ of the slots are filled by girls. Then you have only $P-5$ slots to be filled by $N-4$ boys and $M-1$ girls. ATM, I'm forgetting how you to count that.2012-02-18
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    @Jeff: Unfortunately, without substantial adjustment, this approach won't work. In general it overcounts the number of choices. The idea would work for the related problem of choosing $P$ balls from $M$ green and $N$ red, with the restrictions of the problem, where balls of the same colour are *indistinguishable*.2012-02-18
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    The title should give some indication of the actual question.2012-02-18

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