Question -
Answer -
Given:
The word ‘INVOLUTE’
Total number ofletters = 8
Total vowels are = I,O, U, E
Total consonants = N,V, L, T
So number of ways toselect 3 vowels is 4C3
And numbre of ways toselect 2 consonants is 4C2
Then, number of waysto arrange these 5 letters = 4C3 × 4C2 ×5!
By using the formula,
nCr = n!/r!(n – r)!
4C3 = 4!/3!(4-3)!
= 4!/(3! 1!)
= [4×3!] / 3!
= 4
4C2 = 4!/2!(4-2)!
= 4!/(2! 2!)
= [4×3×2!] / (2! 2!)
= [4×3] / (2×1)
= 2 × 3
= 6
So, by substitutingthe values we get
4C3 × 4C2 ×5! = 4 × 6 × 5!
= 4 × 6 × (5×4×3×2×1)
= 2880
∴ The no. of wordsthat can be formed containing 3 vowels and 2 consonants chosen from ‘INVOLUTE’is 2880.