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

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