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

There are 4 vowels namely, I, O, E, U
and 4 consonants, namely N, V, L, T
`therefore` 3 out of 4 vowels an be selected in `.^(4)C_(3)=4` ways
2 out of 4 consonants can be selected in `.^(4)C_(2)=6` ways
`therefore` Number of combinations of 3 vowels and 2 consonants `= 4xx6=24`
Now in each of these 24 combinations, 5 letters can be arranged among themselves in 5! ways
= 120 ways.
`therefore` Required number of different words `= 24xx120 =2880`.