# Distributing identical balls into identical boxes [closed]

How many ways to distribute 11 identical balls into 3 identical boxes with each box having 2 balls at least

## closed as off-topic by Shailesh, Watson, hardmath, Henrik, NamasteJul 25 '16 at 18:23

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• Any thoughts? Hint: Since each box has at least $2$, you really only have $5$ balls to distribute. How many ways can $5$ be written as the sum of three non-negative integers? – lulu Jul 25 '16 at 12:28
• I assume you want to know the probability of each box having at least 2 balls? Or do you just want to know how many ways that can happen? Have you tried anything? As written, your "question" is likely to get closed unless you add more details. – jdods Jul 25 '16 at 12:30

The ways in which five can be expresses as the sum of three non-negative integers (where order does not matter) are: $$5+0+0$$ $$4+1+0$$ $$3+2+0$$ $$3+1+1$$ $$2+2+1$$
So, number of ways$=5$.