The word $\mathrm{MULTIPLE}$ consists of three vowels that are placed at the ${\mathrm{2}}^{\mathrm{nd} }, 5^{\mathrm{th}}$ and $8^{\mathrm{th}}$ position.

The three vowels can be arranged at their respective places in $3!$ ways.

The remaining $5$ consonants can be arranged at their respective places in $\frac{5!}{2!}=60$ ways

$\therefore$ Total number of arrangements $=3!\times \frac{5!}{2!}=360$