SOLUTION: A caterer is arranging a row of desserts. The row will contain 8 platters of cookies, 5 trays of fruit, and 3 pies. In how many distinct ways can the cookies, fruit, and pies, be a

Hi
16 desserts: 13  cookies and fruit offerings (not exactly the same),
3 pies identical. 
(Similar to distinct ways of arranging letters in a word when 3 of the letters are the same)
distinct ways of arranging in a row:  16!/3!
Wish You the Best in your Studies.

As I understand/interpret this problem, there are 8 + 5 + 3 = 16 items, in all.



Of them, 8 platters are identical (indistinguishable; cookies, letter C);

         5 other platters are identical (indistinguishable; fruits, letter F);

         3 other platters are identical (indistinguishable; pies, letter P).


The question is, how many distinguishable arrangements of these letters/items
of the length 16 can be made ?



Same as to ask how many distinguishable words of the length 16 can be arranged having 8 identical letters C; 

5 identical letters F  and  3 identical letters P.



The answer is   =  = 720720.