(B) The word $VOWEL$ consists of $5$ distinct letters: $V, O, W, E, L$. There are $2$ vowels: $O$ and $E$. Since the vowels must always remain togethe

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(B) The word $VOWEL$ consists of $5$ distinct letters: $V, O, W, E, L$. There are $2$ vowels: $O$ and $E$. Since the vowels must always remain together,we treat $(OE)$ as a single unit. Now,we have $4$ units: $V, W, L, (OE)$. These $4$ units can be arranged in $4! = 24$ ways. The $2$ vowels within the unit $(OE)$ can be arranged in $2! = 2$ ways. Therefore,the total number of words is $24 \times 2 = 48$.

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

Medium

The number of words that can be formed using the letters of the word $VOWEL$ such that the vowels always remain together is

AP EAMCET 2023 All AP EAMCET

A
$60$
B
$48$
C
$36$
D
$45$

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Permutations and Combinations

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

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The number of words that can be formed using the letters of the word $VOWEL$ such that the vowels always remain together is

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