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anonymous
 3 years ago
Number of ways of distributing \(n\) identical things among \(r\) persons when each person can get any number of things.
@Zarkon
anonymous
 3 years ago
Number of ways of distributing \(n\) identical things among \(r\) persons when each person can get any number of things. @Zarkon

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Usually it should be \(\binom{n}r\) but since each person can get any number of things including zero. I made it \(\binom{n+r}{r}\) but in the book it's given \(\binom{n+r1}{r}\)

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.2I believe this could be solved with the equation \[x_1+x_2+...+x_r=n.\]Where every \(x_i\) gets an integer greater than or equal to 0. Solving this problem is well known as the "Stars and Bars" problem and is given by \[\left(\!\!\binom{n}{r}\!\!\right)=\binom{n+r1}{r}\] You have that \(1\) because that's how many symbols you have if you write out every integer as a star, and every plus sign as a bar.

Zarkon
 3 years ago
Best ResponseYou've already chosen the best response.1http://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Thank you. Please medal eachother.
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