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

Asked by Aaryan | 1 year ago |  159

##### Solution :-

Given:

The word ‘INVOLUTE’

Total number of letters = 8

Total vowels are = I, O, U, E

Total consonants = N, V, L, T

So number of ways to select 3 vowels is 4C3

And numbre of ways to select 2 consonants is 4C2

Then, number of ways to arrange these 5 letters = 4C3 × 4C2 × 5!

By using the formula,

nCr =$$\dfrac{ n!}{r!(n – r)!}$$

4C3 = $$\dfrac{4!}{3!(4-3)!}$$

=$$\dfrac{ [4×3!] }{ 3!}$$

= 4

4C2 = $$\dfrac{ 4!}{2!(4-2)!}$$

= $$\dfrac{ (4×3×2!) }{(2! 2!)}$$

= 2 × 3

= 6

So, by substituting the values we get

4C3 × 4C2 × 5! = 4 × 6 × 5!

= 4 × 6 × (5×4×3×2×1)

= 2880

The no. of words that can be formed containing 3 vowels and 2 consonants chosen from ‘INVOLUTE’ is 2880.

Answered by Sakshi | 1 year ago

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