1. Counting Permutations When Indistinguishable Objects May Exist
How many rows , each one consisting of 3 A’s 1 B, and 4 C’s are there?
(Here are some such rows:
BACCCAAC
ABCACACC
CCCCAAAB
Etc.)
Answer: (3+1+4)! / (3!1!4!).

2. In general:
k distinct types of objects are given, where k is a positive integer.
Positive integers ni for i=1,…k are given. k is
a given positive integer. How many rows are there, each one including ni objects of type i
for i=1, …, k and no other objects?
Answer: Let n=n1 + … +nk. Then the number of rows is n!/(n1! … nk!).