SOLUTION: the number of ways in which four letters of the word 'MATHEMATICS'can be arranged .answer is 2454 pls solve this

Question 658540: the number of ways in which four letters of the word 'MATHEMATICS'can be arranged .answer is 2454 pls solve this

Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
I assume, for ordered combinations (i.e. permutations).
Removing the duplicate , and , we have different letters from which we can make
[8]P[4]= permutations.
We need to words having two 's and two other distinct letters:
Pick two spots for the 's ([4]C[2] ways) and then assign the other letters the two other spots ([7]P[2]).
So, we have ([4]C[2])([7]P[2]) = more possibilities.
We do the same for words with two 's and those with two 's, so we're now at .
We also need to words having pairs of like MAMA and TAAT...
For two 's and two 's, there are [4]C[2]= possibilities. Same for 's and 's, and same for 's and 's.
This add to our total.
so, we have

Answer:

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