Question

How many arrangements of the letters of the word SHLOKA can be made such that all vowels are together?

Answer 1

O and A are two vowels in the word SHLOKA-

There are 6 letters in the word SHLOKA of which 2 are vowels.

Considering 2 vowels as one letter, total 5 letters can be arranged in P₅ ways and in each of these arrangements two vowels can be arranged among themselves in P₂ ways.

∴ Total permutations = ⁵P₅ × ³P₃ = 5 ! × 2!

= 120 × 2 = 240