SOLUTION: If the letter 'Daughter' are to be arranged so that vowels occupy odd places, then number of different word are

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Question 658958: If the letter 'Daughter' are to be arranged so that vowels occupy odd places, then number of different word are
Answer by Edwin Parker(36)   (Show Source): You can put this solution on YOUR website!

[There are only 3 vowels, a,u, and e, and there are 4 odd places.  So
one of the odd spaces must contain a consonant.]

we can choose 3 of the 4 odd places to put the vowels in C(4,3) or 4 ways.

For each of those we can rearrange the vowels in P(3,3) or 3! or 6 ways.

And we can rearrange the 5 consonants in P(5,5) or 5! or 120 ways.

C(4,3)稰(3,3)稰(5,5) = 4򉼭20 = 2880 ways.

Edwin
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