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 is \(n\), find the sum of the digits of \(n\).
###### Image credit: Flickr PopCultureGeek

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