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.
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