Question

In how many ways can $5$ identical balls be arranged in $3$ boxes?

Answer 1

Given that ,

5 identical balls be arrange in 3 box

Find number of way =?

Hence ,

$n=5,r=3$

Now ,

Total number of way are

${=}^{n+r-1}{C}_{r-1}{=}^{5+3-1}{C}_{3-1}{=}^7{C}_2$

$=\frac{7!}{(7-2)!2!}=\frac{7\times 6\times 5!}{5!2!}=\frac{7\times 6}{2\times 1}=21$

Hence this is the answer