Question 1023137: Find the number of distinguishable permutations of the given letters "AAABBBCC".
Answer by mathmate(429)   (Show Source):
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Question:
Find the number of distinguishable permutations of the given letters "AAABBBCC".
Solution:
The number permutation from a pool with identical items is given by
(a+b+c)!/(a!b!c!).
where a,b,c are the number of identical items of each kind.
For example, 2 apples 2 pears and 3 oranges can be arranged in
(2+2+3)/(2!2!3!)=210 ways.
Here, there are 3 A's, 3 B's and 2 C's, so
a=3, b=3, c=2
and the number of arrangements (permutations) is
(3+3+2)!/(3!3!2!)= 560.
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