Q. 25.0( 3 Votes )

# How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?

Answer :

In the word ‘INVOLUTE’ there are 4 vowels, ‘I’,’O’,’U’ and ‘E’ and there are 4 consonants, ‘N’,’V’,’L’ and ‘T’. 3 vowels out of 4 vowels can be chosen in ^{4}C_{3} ways. 2 consonants out of 4 consonants can be chosen in ^{4}C_{2} ways. Length of the formed words will be (3 + 2) = 5. So, the 5 letters can be written in 5! Ways. Therefore, the total number of words can be formed is = (^{4}C_{3} X ^{4}C_{2} X 5!) = 2880.

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