Question

How many words can be formed with the letters of the word ‘MATHEMATICS’ by rearranging them?

• A. $\frac{11!}{(2!\times 2!)}$
• B. $\frac{11!}{2!}$
• C. $\frac{11!}{(2!\times 2!\times 2!)}$
• D. $11!$

Answer 1

The correct option is C

$\frac{11!}{(2!\times 2!\times 2!)}$

Explanation for the correct option:

Finding arrangement:

Total number words in ‘MATHEMATICS’ is $11$

Therefore arrangement will be $11!$

But letter ‘M, T & A’ are repeated twice therefore their arrangement is given by $2!$ for each letter

Arrangement $\mathbf{=}\frac{\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{m}\mathbf{u}\mathbf{t}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{n}\mathbf{o}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{w}\mathbf{o}\mathbf{r}\mathbf{d}\mathbf{s}\mathbf{}}{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{}\mathbf{o}\mathbf{f}\mathbf{}\mathbf{w}\mathbf{o}\mathbf{r}\mathbf{d}\mathbf{s}\mathbf{}\mathbf{r}\mathbf{e}\mathbf{p}\mathbf{e}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{d}}$

Total number word form by the letter of ‘MATHEMATICS’ is $\frac{11!}{(2!\times 2!\times 2!)}$

Hence, the correct option is $\left(C\right)$