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How many ways are there to distribute 4 identical oranges and 6 distinct apples into 5 distinct boxes

I know you find number of ways for apples which is 5^6.

The solution tells me that the ways for oranges is 8 choose 4.

You then multiply both of them together to get solution, which is 1,093,750

My question is....where does 8 come from, for 8 choose 4???

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  • $\begingroup$ Yeah, that looks like a typo. $\endgroup$ – Eric Stucky Oct 19 '14 at 23:43
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You should look at the technique of Stars and Bars, also known as using identical dividers.

In this case, we use 4 dividers to simulate distributing the oranges amongst 5 boxes.

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