Question

The number of permutation that can be made out of the letters of the word "MATHEMATICS" when the relative positions of vowels and consonants remain un altered is

• A. $3\times 7!$
• B. $2\times 7!$
• C. $7!$
• D. $4\times 7!$

Answer 1

The correct option is A $3\times 7!$

Since we have to keep the position of vowels and consonants fixed while arranging, we will arrange them individually
$\therefore$ Required number of ways is $\frac{4!}{2!}\times \frac{7!}{2!\times 2!}=3\times 7!$