How many words can be formed from the letters of the word quot ALTER quot so that the vowels never c...........

Quantitative Aptitude ( CCS) Permutation & Combination

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

None of these

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Explanation:

We need to find the ways that vowels never come together.
Vowels are A, E
Let the word be LTR(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