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Larry, Michael, and Doug have five donuts to share. If any [#permalink]
19 May 2006, 22:22
Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
In general this problem can take multiple forms
1. how many ways can u separate N numbered balls (1..N) into X buckets
2. How many ways can u separate N identical balls into X buckets.
3. How many ways can u add X numbers to get N as the sum where
a) 1 or more numbers can be 0
b) Each number is > 0.
3) I am not sure I understood this question. Please explain.
Should have been obvious.
3a) How many ways can we get distinct non-negative integers (x1,x2,x3,x4...xr) such that x1+x2+x3..xr = N where N is another distinct non-negative number.
Solved the same way as separating N identical balls into R urns.
b) Here we just add the condition that x1,x2,x3 are all greater than 0.
We can again solve this as the urns+balls problem i.e the number of ways of placing N balls into R urns with each urn having at least one ball. Keep the N balls in a row. We get N-1 spots between the balls which is a demarcator. We'll now choose (R-1) spots from the N-1 spots.