Question

How many words can be formed with the letters of the word MATHEMATICS by rearranging them.

• A. $\frac{11\mspace{6mu}!}{2\mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!}$
• B. $\frac{11\mspace{6mu}!}{2\mspace{6mu}!}$
• C. $\frac{11\mspace{6mu}!}{2\mspace{6mu}!\mspace{6mu} 2 ⥂ \mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!}$
• D. $11\mspace{6mu}!$

Answer 1

Answer: (C)

$\frac{11\mspace{6mu}!}{2\mspace{6mu}!\mspace{6mu} 2 ⥂ \mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!}$

Answer 2

Since there are 2 M's, 2 A's and 2T's.

$\therefore$ Required number of ways are $\frac{11\mspace{6mu}!}{2\mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!\mspace{6mu} 2\mspace{6mu}!}$.