## Ishaan94 Group Title Number of ways of distributing $$n$$ identical things among $$r$$ persons when each person can get any number of things. @Zarkon 2 years ago 2 years ago

1. Ishaan94

Usually 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 $$\binom{n+r-1}{r}$$

2. Zarkon

stars and bars ;)

3. KingGeorge

I 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 $\left(\!\!\binom{n}{r}\!\!\right)=\binom{n+r-1}{r}$ 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.

4. Zarkon
5. Ishaan94