SOLUTION: How many permutations are there of the following word. Mathematics

Question 638094: How many permutations are there of the following word. Mathematics
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
mathematics has 11 letters.
there are 2 instances of m.
there are 2 instances of a
there are 2 instances of t
i think that's all the multiple occurrences in that word.
the formula is 10! / (2!*2!*2!) which gets you 10!/8 which gets you 453600.

you divide by 2! because there are 2 instances of m.
you divide by 2! because there are 2 instances of a.
you divide by 2! because there are 2 instances of t.

to see what happens, assume 3 letters.
assume abc.
no duplicates there so the number of possible permutation is 3! which is 6.
since the numbers are small, we can show them.
abc
acb
bac
bca
cab
cba
those are the 6 possible permutations.
now assume the c is really an a.
your letters are now aba
the number of permutations becomes 3!/2! = 3.
those permutations are:
aba
aab
baa
where you might have had abc and cba, you now have aba.
where you might have had acb and cab, you now have aab.
where you might have hade bac and bca, you now have baa.
the permutations that were 3*2*1 are now 3*2*1/2 = 3*1.
the permutations that would have been a and c had to be removed because they no longer existed once we set c equal to a.

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