How many arrangements of the word “DETAIL” place vowels only in odd positions? | Aspire Study

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Qus

How many arrangements of the word “DETAIL” place vowels only in odd positions?

1
2
3
4

Solution

Vowels = E, A, I → 3 vowels Odd positions = 1, 3, 5 → 3 positions Ways: $ 3! \text{ (vowels)} \times 3! \text{ (consonants)} = 6 \times 6 = 36 $

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