Answer :

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 N_{1}.

⇒ N_{1} = (No. of ways of choosing 3 vowels from 4 vowels) × (No. of ways of choosing 2 consonants from 4 consonants)

⇒ N_{1} = (^{4}C_{3}) × (^{4}C_{2})

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N_{1} = 4 × 6

⇒ N_{1} = 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 = N_{1} × 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.

Rate this question :

There are 1RD Sharma - Mathematics

How many diRD Sharma - Mathematics

A committeeRD Sharma - Mathematics

How many woRD Sharma - Mathematics

A paralleloRD Sharma - Mathematics

How many woRD Sharma - Mathematics

In an examiRD Sharma - Mathematics

Out of 18 pRD Sharma - Mathematics

A committeeRD Sharma - Mathematics

How many woRD Sharma - Mathematics