Question

Total number of ways in which 256 identical balls can be placed in 16 numbered boxes (1,2,3,.,16) such that $r^{th}$ box contains at least r balls is $(1\le r\le 16)$

• A. ${}^{120}{C}_{15}$
• B. ${}^{119}{C}_{15}$
• C. ${}^{256}{C}_{15}$
• D. ${}^{255}{C}_{15}$

Answer 1

The correct option is B ${}^{119}{C}_{15}$

If we put minimum number of balls required in each box, then remaining 120 balls can be put in ${}^{119}{C}_{15}$ ways without any restriction.