Question

The number of words that can be formed by using the letters of the word $"MATHEMATICS"$, taken all at a time is:

• A. $11!$
• B. $\frac{11!}{2!+2!+2!}$
• C. $\frac{11!}{(2!{)}^3}$
• D. $noneofthese$

Answer 1

The correct option is C $\frac{11!}{(2!{)}^3}$

Number of words that can be formed by using word Mathematics. taken all at a time.

$\to$ Mathematics $\to 11$ letter.

No of $M\to 2$

No of $A\to 2$

No of $t\to 2$

taken this number as a group

MM AA tt , h, e, i, c, s

$\to$ the number of ways $=\frac{11!}{2!2!2!}$

$=\frac{11!}{(2!{)}^3}$