Question

Consider the letters of the word $MATHEMATICS$. Possible number of words taking all letters at a time such that at least one repeating letter is at odd position in each word is

• A. $\frac{11!}{2!2!2!}-\frac{9!}{2!2!}$
• B. $\frac{9!}{2!2!2!}$
• C. $\frac{9!}{2!2!}$
• D. $\frac{11!}{2!2!2!}$

Answer 1

The correct option is D $\frac{11!}{2!2!2!}$

Since there are $5$ even places and $3$ pairs of repeated letters, therefore at least one of these must be at an odd place. Therefore, the number of ways is $11!/(2!2!2!)$.