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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
I assume, for ordered combinations (i.e. permutations).
Removing the duplicate M,+A and T, we have 8 different letters from which we can make
[8]P[4]=+8%21%2F4%21=+1680 permutations.
We need to add words having two M's and two other distinct letters:
Pick two spots for the M's ([4]C[2] ways) and then assign the 7 other letters the two other spots ([7]P[2]).
So, we have ([4]C[2])([7]P[2]) = 6+%2A+42+=+252 more possibilities.
We do the same for words with two A's and those with two T's, so we're now at 1680+%2B+3%2A252+=+2436.
We also need to add words having pairs of identical+letters like MAMA and TAAT...
For two M's and two A's, there are [4]C[2]=6 possibilities. Same for M's and T's, and same for A's and T's.
This add 18 to our total.
so, we have
2436%2B18=2454
Answer: 2454