Question

In how many other ways can the letters of the word ${}^{\prime }MULTIPL{E}^{\prime }$ be arranged without changing the relative positions of vowels and consonants

• A. $256$
• B. $360$
• C. $359$
• D. $242$

Answer 1

The correct option is C $359$

The word $MULTIPLE$ has $3$ vowels $\xi$ $5$ consonants.

Their relative positions must not be changed.

$\Rightarrow$ Vowels lie in $2nd,5th,8th$ place $\xi$ consonants in the remaining.

$\Rightarrow$ Vowels can be arranged in $3!$ ways $=6$

$\Rightarrow$ Consonants can be arranged in $\frac{5!}{2!}$ ways $=60$

$\Rightarrow$ Total $=6\times 60=360$

$\Rightarrow$ Required $=360-1=359$ (excluding $multiple$ )

Hence, the answer is $359.$