Question

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE ?

Answer 1

I N V O L U T E

Number of letters = 8

Vowels = I, O, U, E

Consonants = N, V, L, T,

Number of ways to select 3 vowels $={}^4{C}_3$

Number of ways to select 2 consonants $={}^4{C}_2$

Number of ways to arrange these five letters

$={}^4{C}_3{\times }^4{C}_2\times 5!$

$=4\times 6\times 5\times 4\times 3\times 2\times 1$

$=2880$

Required number of ways $=2880$