How many words with or without meaning each of three vowels and two consonants can be formed from the letters of the word INVOLUTE.

Explanation

In the word INVOLUTE, there are 4 vowels, namely, I,O,E,U and 4 cónsonants, namely, `N, V, L` and `T`

The number of ways of selecting 3 yowels out of `4= ^4 C_3=4`
The number of ways of selecting 2 consonanits out of `4= ^4 C_2=6`
Therefore, the number of combinations of 3 vowels and 2 consonants is `4 xx 6=24`
Now, each of these 24 combinations has 5 letters which cạn be.arranged among themselves in `5 !` ways.
Therefore, the required number of different words is `24 xx 5 !=2880`.