The number of words that can be formed using the letters a,b,c,d,e,f taken 3 together each containing atleast one vowel is :

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answer is C.

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Detailed Solution

Let us separate the vowels and consonants from the given word
Vowels={a,e}
Consonants={b,c,d,f}
There are two vowels hence there are two cases -one vowel +2 consonant words and two vowels +1 consonant words.
Case 1:
One vowel out of 2 vowels can be arranged in 2C1=2 ways
The number of ways 2 consonants can be selected is 4C2=6 ways
The number of ways the three letters can be arrange is 3!=6 ways
The total number of ways is 266=72 ways
Case 2:
Two vowels out of 2 vowels can be arranged in 2C2=1 ways
The number of ways 1 consonant can be selected is 4C1=4 ways
The number of ways the three letters can be arrange is 3!=6 ways
The total number of ways is 146=24 ways
Hence the total number of ways =72+24=96 ways

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