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???

  • $\begingroup$ Yeah, that looks like a typo. $\endgroup$ – Eric Stucky Oct 19 '14 at 23:43

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.