Calculating number of non-duplicated permutation

Question

I want to calculate the number of permutation from duplicated list.

Example) There is a list combined of 76 icons.

Here is icon list

A: 1 B: 3 C: 5 D: 6 E: 6 F: 5 G: 10 H: 9 I: 8 J: 7 K: 6 L: 10

In this List, I want to pick 3 icon and make a permutation list without duplication. For example (B,B,C), (C,B,B), (B,C,B) will be counted as different case.

Thank you.

Answer 1

Hint: If you don't use $A$, how many choices do you have for each slot? You have enough of each that you won't run out. If you do use $A$, put it somewhere, then fill the other slots.