How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?
Given the word is INVOLUTE. We have 4 vowels namely I,O,U,E, and consonants namely N,V,L,T.
We need to find the no. of words that can be formed using 3 vowels and 2 consonants which were chosen from the letters of involute.
Let us find the no. of ways of choosing 3 vowels and 2 consonants and assume it to be N1.
⇒ N1 = (No. of ways of choosing 3 vowels from 4 vowels) × (No. of ways of choosing 2 consonants from 4 consonants)
⇒ N1 = (4C3) × (4C2)
We know that ,
And also n! = (n)(n – 1)......2.1
⇒
⇒
⇒
⇒ N1 = 4 × 6
⇒ N1 = 24
Now we need to find the no. of words that can be formed by 3 vowels and 2 consonants.
Now we need to arrange the chosen 5 letters. Since every letter differs from other. The arrangement is similar to that of arranging n people in n places which are n! ways to arrange. So, the total no. of words that can be formed is 5!.
Let us the total no. of words formed be N.
⇒ N = N1 × 5!
⇒ N = 24 × 120
⇒ N = 2880
∴ The no. of words that can be formed containing 3 vowels and 2 consonants chosen from INVOLUTE is 2880.