(B) The total number of letters is $6$ $(a, b, c, d, e, f)$. The vowels are $a, e$ ($2$ vowels) and the consonants are $b, c, d, f$ ($4$ consonants).T

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(B) The total number of letters is $6$ $(a, b, c, d, e, f)$. The vowels are $a, e$ ($2$ vowels) and the consonants are $b, c, d, f$ ($4$ consonants).Total arrangements of $3$ letters from $6$ letters without repetition is $^6P_3 = 6 \times 5 \times 4 = 120$.Arrangements with no vowels (i.e.,all $3$ letters are consonants) is $^4P_3 = 4 \times 3 \times 2 = 24$.Therefore,the number of arrangements with at least one vowel is $120 - 24 = 96$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

A
$72$
B
$96$
C
$24$
D
$128$

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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How many arrangements of $3$ letters can be made from the letters $a, b, c, d, e, f$ without repetition,such that each arrangement contains at least one vowel?

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