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How many functions map nothing to a j-element subset j of k

Question: How many functions map nothing to a j-element subset J of K? Another way to say this is if I have n distinct candy bars and k children Sam, Mary, Pat, etc., in how many ways may I pass out the candy bars so that some particular j-element subset of the children don't get any (and maybe some other children don't either)?

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Mathematics: How many functions map nothing to a j-element subset j of k

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