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Q.
If the number of all possible permutations of the letters of the word MATHEMATICS in which the repeated letters are not together is $982(X)$, then $X=$
TS EAMCET 2020
Solution:
Total number of words that can be formed with the letters of the word 'MATHEMATICS'
$=\frac{11 !}{2 ! 2 ! 2 !}=4989600$
Number of words in which all the repeated letters are together
$=8 ! \times \frac{2 !}{2 !} \times \frac{2 !}{2 !} \times \frac{2 !}{2 !}=8 !=40320$
$\therefore $ Required words $=4989600-40320=4949280$
It is given that $982(X)=4949280$
$\Rightarrow X=\frac{4949280}{982}=5040$