How many words can be formed from the letters of the word AFTER, so that the vowels never come together ?

A. 48

B. 52

C. 72

D. 120

Answer : C. 72

Explanation:

We need to find the ways that vowels NEVER come together.
Vowels are A, E Let the word be FTR(AE) having 4 words.
Total ways = 4! = 24
Vowels can have total ways 2! = 2
Number of ways having vowel together = 48
Total number of words using all letter = 5! = 120.
Number of words having vowels never together = 120 – 48 = 72

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