Question
In how many different ways can the letters of the word
‘PUBLIC’ 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 2 vowels and 4 consonants. Now, 2 vowels can be placed at any of the three places out of 3 odd positions. Number of ways of arranging the vowels = 3P2 = 3 Also, the 4 consonants can be arranged at the remaining 4 positions. Number of ways of arranging the consonants = 4P4 = 4! Total number of ways = (3 × 4!) = 72
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