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Question: The no. of ways in which n<sup>2</sup> identical balls can be put in n numbered boxes (1, 2, 3, ……, ...

The no. of ways in which n2 identical balls can be put in n numbered boxes (1, 2, 3, ……, n) such that ith box contains at least i number of balls is-

A

n2Cn−1n^{2}C_{n - 1}

B

n2−1Cn−1n^{2} - 1C_{n - 1}

C

n2+n−2Cn−1n^{2} + n - 2C_{n - 1}

D

None

Answer

n2+n−2Cn−1n^{2} + n - 2C_{n - 1}

Explanation

Solution

If we put minimum no. of balls required in each box, balls left are n(n−1)2\frac{n(n - 1)}{2}which can be put in n boxes in n2+n−2Cn−1n^{2} + n - 2C_{n - 1}ways without any restriction.