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(20850) (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:

RELATED QUESTIONS
find the number of ways in which an arrangement of of 4 letters can be made from the word (answered by jrfrunner)

in how many different ways can the letters of word "MATHEMATICS" be arranged so that... (answered by Edwin McCravy)

The number of ways in which we can arrange 4 letters of the word mathematics is given by (answered by jim_thompson5910)

find the number of ways of selecting four letters from the word 'EXAMINATION'.ANSWER IS... (answered by MathLover1,kevwill)

Consider the letters of the word "TOMORROW". find the number of ways in which four... (answered by Edwin McCravy,ikleyn)

in how many ways can the letters of the word PERIMETER be arranged? also arrange four... (answered by stanbon)

Find the number of ways in which the 7 letters of the word PYRAMID can be arranged in a... (answered by Fombitz)

(a) In how many different ways can the letters in the word ARRANGEMENTS be arranged?... (answered by math_helper,ikleyn)

In how many ways can the letters of the word "little" be... (answered by nyc_function)