Question
In how many different ways can the letters of the word
‘NATURE’ be arranged in such a way that the vowels occupy only the odd positions?Solution
There are 6 letters in the given word out of which there are 3 vowels and 3 consonants. Now, 3 vowels can be placed at any of the three places out of 3 odd positions. Number of ways of arranging the vowels = 3P3 = 3! Also, the 3 consonants can be arranged at the remaining 3 positions. Number of ways of arranging the consonants = 3P3 = 3! Total number of ways = (3! × 3!) = 36
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