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# The number of all possible arrangements of the letters of the word’MATHEMATICS’taken four at time is?

Ravi
7 years ago
You can assume as if you have 4 void spaces to be filled with the letters of the word ‘MATHEMATICS’. In all you have how many distinct letters has to be calculated first.

M=2
A=2
T=2
H=1
E=1
I=1
C=1
S=1 are all the letters with which the word has been formed. Hence, for filling the void spaces,
Starting with the first blank, you have
11 choices, for first blank
10 for second
9for 3rd
and 8 for 4th .
But as there are repeatations in the arrangements as some letters are repaeated in the word itself. So dividing the number of arr. by the number of repeatations for letters appearing more than once i.e. (2.2.2)

And obtain the answer for the case when each letter has to be used just once