Exams Joint Entrance Examination Mathematics Permutations and Combinations Question 232 Question 232 of 278 Medium MCQ
The number of arrangements that can be formed from the letters a , b , c , d , e , f a,b,c,d,e,f a , b , c , d , e , f taken 3 at a time without repetition, and each arrangement containing at least one vowel, is:
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Vowels: a , e a,e a , e (2); consonants: b , c , d , f b,c,d,f b , c , d , f (4).
Exactly 1 vowel: ( 2 1 ) ( 4 2 ) × 3 ! = 2 × 6 × 6 = 72 \binom21\binom42\times3! = 2\times6\times6 = 72 ( 1 2 ) ( 2 4 ) × 3 ! = 2 × 6 × 6 = 72
Exactly 2 vowels: ( 2 2 ) ( 4 1 ) × 3 ! = 1 × 4 × 6 = 24 \binom22\binom41\times3! = 1\times4\times6 = 24 ( 2 2 ) ( 1 4 ) × 3 ! = 1 × 4 × 6 = 24
\[\text{Total} = 72+24 = 96\] Answer the question to unlock