Question

How many words can be formed out of 10 consonants and 4 vowels, such
that each contains 3 consonants and 2 vowels ?
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Answer 1

Answer:

Total no. of consonants = 10

no. of consonants to be chosen = 3

no. of ways of choosing 3 consonants = C (10,3)

= 10!/3!(10-3)! = 10!/3!7! = (10 × 9 × 8 × 7!)/ 3! × 7!

= (10 × 9 × 8)/3! = (10 × 9 × 8)/3 × 2 = 5 × 3 × 8 = 15 × 8 = 120 ways

Total no. of vowels = 4

no. of vowels chosen = 2

no. of ways of choosing vowels = C (4,2)

= 4!/2! (4-2)! = 24/2×2 = 6 ways

No. of ways of forming words = 120 × 6 = 720