Question
In how many ways can the letters of the word
āEDUCATIONā be arranged such that the vowels take the odd positions?Solution
According to the question,
There are 5 odd positions and 5 vowels, all distinct: E, U, A, I, O
Therefore, number of ways of arranging the 5 vowels in odd positions = 5! = 120 ways
The remaining 4 consonants (D, C, T, N) can be arranged in the even positions = 4! = 24 ways
Required number of ways = 120 Ć 24 = 2880
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