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How many arrangements can be formed out of the letters of the word EXAMINATION so that vowels always occupy odd places?
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! Â Â Â Â Â Â (2)
Now total arrangements = (1)*(2)
=10,800
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