Question

No. Of ways in which 12 identical balls can be put in 5 different boxes in a row, if no box remains empty is

• A. ${}^{10}{C}_4$
• B. ${}^{11}{C}_4$
• C. ${}^{12}{C}_4$
• D. ${}^9{C}_4$

Answer 1

The correct option is B ${}^{11}{C}_4$

This is same as placing 4 sticks anywhere in the 11 gaps created by placing 12 balls in a row such that no 2 sticks are put in the same gap. Therefore we have 11 gaps and 4 sticks.
${}^{(n-1)}{C}_{r-1}$
= ${}^{\left(11\right)}{C}_4$