SOLUTION: How many ways can the letters in the word AGATHIST be rearranged? Any help will be appreciated!

Question 1029840: How many ways can the letters in the word AGATHIST be rearranged?
Any help will be appreciated!
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
How many ways can the letters in the word AGATHIST be rearranged?
Any help will be appreciated!

Solution:
the number of permutations is given by
n!/(n1!n2!n3!...nk!)
where each of n1, n2... is the number of occurrences of each letter.
Making a count of each letter:
A 2
G 1
H 1
I 1
S 1
T 2
total 8.
So the number of permutations is
8!/(2!1!1!1!1!2!)=40320/4=10080

The same formula can also be used to solve problems of permutation of multiple coloured balls.

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