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Discrete math

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There are eighteen guard posts. How many ways can 25 not indistinguishable (That is, they are distinguishable.)guards be distributed to the guard posts, so that no post is empty?

Try - (25 choose 18) ??

  • Discrete math -

    Think of it this way:

    Every time all the 18 posts are filled, there will be a set of 7 guards left out.
    So the question becomes, how many set of 7 from 25 can we find, which is
    C(25,7) or C(25,8) , both yield the same answer.

    BTW, your clarification in brackets is a contradiction
    you probably meant to say
    ((That is, they are NOT distinguishable.)

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