How many words can be formed out of the letters of the word, ORIENTAL, – InterviewSolution

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1.	How many words can be formed out of the letters of the word, ORIENTAL,so that the vowels always occupy the odd places?
Answer» Correct Answer - 576 The given word contains 4 vowels and 4 consonants. Let us fix the 8 place as shown below. `(""^(1))(""^(2))(""^(3))(""^(4))(""^(5))(""^(6))(""^(7))(""^(8))` The 4 vowels can be arranged at 4 places (namely 1, 3, 5, 7) in ` ""^(4)P_(4)=4! =24` ways. And, the 4 consonants can be arranged at 4 places (namely 2, 4, 6, 8) in `""^(4)P_(4) =4! =24` ways. Required number of ways `=(24xx24)=576.`

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