$n$ , find the sum of the digits of $n$ .

Cruella De Vil has 15 dalmations captive. She wishes to cage them into 5 distinct cages, with each cage containing 3 puppies. If each dalmatian is distinct, and the number of ways Cruella can arrange the 15 dalmatians in each of the cages isThe answer is 30.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

The answer will be $\dbinom{15}{3}*\dbinom{12}{3}*\dbinom{9}{3}*\dbinom{6}{3}*\dbinom{3}{3} = 168168000$ .Hence the sum of the digits is $1+6+8+1+6+8 = \boxed{30}$ .

$\textbf{Note:}$ You should also have mentioned that the cages are distinct that is the $1st$ $3$ dalmatians going to cage $1$ is different from them going to cage $2$ (say).Had all the cages been similar we would have to divide the whole thing by $5!$ .