Question

Consider the word ${}^{\prime }PERMUTATIO{N}^{\prime }$. How many permutations can be made with all the vowels together?

• A. $\frac{7!}{2!}$
• B. $7!\times 5!$
• C. $\frac{7!\times 5!}{2!}$
• D. None of these

Answer 1

The correct option is C $\frac{7!\times 5!}{2!}$

$PERMUTATION$

Vowels $(a,e,i,o,u)$ $5$

Consonants $6$

Consider all vowels as one unit and

Consider all consonants as one unit

Total $7$ units

Internal arrangement of vowels $=5!$

Total arrangements of units $=\frac{7!\times 5!}{2!}$