Question -
Answer -
Given:
Total number of vowels= 5
Total number ofconsonants = 17
Number of ways = (No.of ways of choosing 2 vowels from 5 vowels) × (No. of ways of choosing 3consonants from 17 consonants)
= (5C2)× (17C3)
By using the formula,
nCr = n!/r!(n – r)!
= 10 × (17×8×5)
= 10 × 680
= 6800
Now we need to findthe no. of words that can be formed by 2 vowels and 3 consonants.
The arrangement issimilar 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!
So, 6800 × 5! = 6800 ×(5×4×3×2×1)
= 6800 × 120
= 816000
∴ The no. of wordsthat can be formed containing 2 vowels and 3 consonants are 816000.