# 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.

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