Question

Find the number of different ways of arranging letters in the word PLATOON if consonants and vowels occupy alternate positions.

Answer 1

When consonants and vowels occupy alternate positions:
There are 4 consonants and 3 vowels in the word PLATOON.
∴ At odd places, consonants occur and at even places, vowels occur.
4 consonants can be arranged among themselves in 4! ways
3 vowels in which O occurs twice and A occurs once.
∴ They can be arranged in `(3!)/(2!)` ways
∴ Required number of arrangements if the consonants and vowels occupy alternate positions
= `4!xx(3!)/(2!)`
= `4xx3xx2xx(3xx2!)/(2!)`
= 72