There are 5 letters of the word MANGO of which two vowels are A and O.
Now, 5 letters of the word MANGO can be arranged in 5P5 = 5! = 120 ways.
Considering two vowels as one letter, total (3 + 1) 4 letters can be arranged in 4P4 ways and in each of these arrangements two vowels can be arranged in 2P2 ways.
∴ Toted permutations in which vowels are together
= 4P4 × 2P2
= 4! × 2!
= 24 × 2 = 48
Now, Total permutations in which two vowels are not together
= Total permutations for arranging all 5 letters] – [Total permutations in which two vowels are together
= 120 – 48 = 72
