How many words, with or without meaning, each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

Explanation

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) ** 4_(C_2)** 5!) = 2880.`