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Question
In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?
Solution
The word INTERMEDIATE consists of 12 letters that include two Is, two Ts and three Es.
There are 6 vowels (I, I, E, E, E and A) that are to be arranged in six even places =\[\frac{6!}{2!3!}\]= 60
The remaining 6 consonants can be arranged amongst themselves in\[\frac{6!}{2!}\]
ways, which is equal to 360.
By fundamental principle of counting, the number of words that can be formed = 60\[\times\]360 = 21600
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