Question

The letters of the word ${}^{\prime }LOGARITH{M}^{\prime }$ are arranged in all possible ways. The number of arrangements in which the relative positions of the vowels and consonants are not changed is

• A. $720$
• B. $3420$
• C. $4200$
• D. $4320$

Answer 1

The correct option is D $4320$

Since the vowels will be fixed at $2nd,4th$ and $6th$ position and they can be interchanged among themselves in $3!$ ways
While the consonants can be arranged in remaining $6$ places in $6!$ ways
$\therefore$ total ways $=3!\times 6!=4320$