Question

The number of different matrices can be formed using all the letters of word $TOMATO,$ is

• A. $720$
• B. $900$
• C. $180$
• D. $360$

Answer 1

The correct option is A $720$

Total elements $=6$
So, possible orders $=1\times 6,6\times 1,2\times 3,3\times 2$
Now, ways of arranging all letters $=\frac{6!}{2!\cdot 2!}$
$=180$
So, total different matrices $=4\times 180=720$