Question

The number of ways in which the letters of the word ${}^{\prime }MADHUR{I}^{\prime }$ can be arranged so that vowels always occupy the beginning, middle and end places is

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

Answer 1

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

$3$ vowels $\{A,U,I\}$ can be arranged in $3$ places in $3!$ ways and the remaining paces can be filled by $4$ consonants in $4!$ ways.
So, required of arrangement of the letters of the word ${}^{\prime }MADHUR{I}^{\prime }$ are $3!\cdot 4!$