Question

Consider the letters of the word MATHEMATICS. There are eleven letters some of them are identical. Letters are classified as repeating and non-repeating letters. Set of repeating letters$\{M,A,T\}$. Set of Possible number of words taking all letters at a time such that atleast one repeating letter is at odd position in each word, is?

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

Answer 1

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

The total no. of letters in the word is $11$

They can be arrange in $11!$ ways

Here they are $3$ identicals letters

The are repeated $2$ times each So the no .of ways is $\frac{11!}{2!2!2!}$