Question

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 $X=$

• A. 5040
• B. 14400
• C. 21600
• D. 86400

Answer 1

Answer: (A)

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 $982(X)=4949280$
$\Rightarrow X=\frac{4949280}{982}=5040$