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Question
In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:
the relative order of vowels and consonants do not alter?
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Solution
The relative positions of all the vowels and consonants is fixed.
Arranging the six vowels at their places, without disturbing their respective places, we can arrange the six vowels in\[\frac{6!}{2!3!}\] ways.
Similarly, arranging the remaining 6 consonants at their places, without disturbing their respective places, we can arrange the 6 consonants in\[\frac{6!}{2!}\] ways.
By fundamental principle of counting, the number of words that can be formed =\[\frac{6!}{2!3!}\] X \[\frac{6!}{2!}\]= 21600
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