How many words, each of 3 vowels and 2 consonants, can be formed from the letters of the word ‘INVOLUTE’?
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 4C3 ways. 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.