Question

How to distribute *(n+1)* different balls into n boxes so
that “no box will be empty”?

Answer #1

**We have to distribute (n+1) different balls into n
boxes, so that no box will be empty.**

**Now, no box would be empty, means we have to put at
least one ball in each box.**

**Let us put one ball each in n boxes; first let us choose
which n balls to put in n boxes, 1 each, out of these n+1
balls.**

**That can be done in ((n+1) C n) ways.**

**Now, this n balls can be put in n boxes, in n! number of
ways.**

**The last ball can be put into any of the n
boxes.**

**So, the number of favourable cases is**

**So, the number of ways in which (n+1) different balls
can be distributed into n boxes, such that no box stays empty,
is**

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