Question

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

Answer 1

In the word INVOLUTE there are 4 vowels (I, O, E, U) and 4 consonants (N, V, L, T) 

Number of ways of selecting 3 vowels out of 4 = ⁴C₃ = 4 

Number of ways of selecting 2 consonants out of 4 = 4C2 =6 

∴ Number of combinations of 3 vowels and 2 consonants is 4 x 6 = 24 

Now, each of these 24 combinations has 5 letters Which can be arranged themselves in 5! Ways 

∴ Required number words = 24 x 5 ! 

= 24 x 120 = 2880