Question

The number of ways in which the letters of the word $MADHURI$ can be arranged so that the vowels always occupy the beginning, middle and end places is

• A. $7!$
• B. $3\cdot {}^4{C}_3$
• C. $4\cdot {}^3{C}_3$
• D. $3!\cdot 4!$

Answer 1

The correct option is D $3!\cdot 4!$

Given word is $MADHURI$
$3$ vowels $\{A,U,I\}$ in $3$ places can be arranged in $3!$ ways
Remaining places can be filled by $4$ consonants in $4!$ ways.
So, the total number of ways
$=3!\cdot 4!$