How many words, with or without meaning each of 3 vowels and 2 consonants can be formed from the letters of the word ‘INVOLUTE’?
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.
Number of selections =
(ii) Select two consonants out of 4.
Number of selections =
(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