Given that we need to find the no. of words formed by 2 vowels and 3 consonants which were taken from 5 vowels and 17 consonants.

Let us find the no. of ways of choosing 2 vowels and 3 consonants and assume it to be N₁.

⇒ N₁ = (No. of ways of choosing 2 vowels from 5 vowels) × (No. of ways of choosing 3 consonants from 17 consonants)

⇒ N₁ = (⁵C₂) × (¹⁷C₃)

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N₁ = 10 × 680

⇒ N₁ = 6800

Now we need to find the no. of words that can be formed by 2 vowels and 3 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 = 6800 × 120

⇒ N = 816000

∴ The no. of words that can be formed containing 2 vowels and 3 consonants are 816000.