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Question
In how many ways can the letters of the word 'STRANGE' be arranged so that
the vowels occupy only the odd places?
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Solution
There are 7 letters in the word STRANGE.
We wish to find the total number of arrangements of these 7 letters so that the vowels occupy only odd positions.
There are 2 vowels and 4 odd positions.
These 2 vowels can be arranged in the 4 positions in 4\[\times\]3 ways, i.e. 12 ways.The remaining 5 consonants can be arranged in the remaining 5 positions in 5! ways.
By fundamental principle of counting:
Total number of arrangements = 12\[\times\]5! = 1440
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