Question 95

How many arrangements can be formed out of the letters of the word EXAMINATION so that vowels always occupy odd places?

Solution

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Number of vowels in word EXAMINATION =6

Number of consonants in word EXAMINATION =5

Number of ways in which 6 vowels can be arranged in 6 odd places=(6!)/2!*2!   (1)

Number of ways in which 5 consonants can be arranged in 5 even places = 5!/2!        (2)
Now total arrangements = (1)*(2)
=10,800

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