Can someone give me a hint on this problem and also can one friend take more than one gift because it is not clear in the statement.
Can someone give me a hint on this problem and also can one friend take more than one gift because it is not clear in the statement.
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You buy exactly one gift for every friend. So in total you buy exactly m gifts. The question is in how many different ways you can choose m out of n gifts. With the extra constraint that at least k of them have a price of at least d.
Divide the n gifts into two groups. One expensive group where every gift has a price of at least d. And one cheap group with all the other gifts.
How many ways there are to choose k gifts out of the expensive gifts and m-k out of the cheap gifts? How many ways to choose k+1 expensive gifts and m-k-1 out of the cheap gifts? ...