Question

The total number of ways in which n² number of identical balls cane be put in n numbered boxed (1, 2, 3, ……n) such that i^th box contains at least i number of balls, is –

• A. $n^{2}C_{n–1}$
• B. $n^{2}–1C_{n–1}$
• C. $\frac{n^{2} + n–2}{2}C_{n–1}$
• D. None

Answer 1

Answer: (C)

$\frac{n^{2} + n–2}{2}C_{n–1}$

Answer 2

If we put minimum number of balls required in each box. Balls left are $\frac{n(n–1)}{2}$ which can be put in $\frac{n^{2} + n–2}{2}C_{n–1}$ ways without restriction.