The word is 'INVOLUTE'
Number of consonants = 4
Number of vowels = 4.
The words formed should contain 3 vowels and 2 consonants.
The problems becomes:
(i) Select 3 vowels out of
4.
(ii) Select two consonants out of 4.
(iii) Arrange the five letters (3 vowels + 2 consonants) to form words.
Number of permutations = 5!
(iv) Apply fundamental principle of counting:
Number of words formed =
=
= 4 x 6 x 120 = 2880
Hence, the number of words formed = 2880
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How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?
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 4C3ways. 2 consonants out of 4 consonants can be chosen in 4C2 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 = (4C3 X 4C2 X 5!) = 2880.