How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?

Asked by Aaryan | 1 year ago |  129

##### Solution :-

Given:

Total number of vowels = 5

Total number of consonants = 17

Number of ways = (No. of ways of choosing 2 vowels from 5 vowels) × (No. of ways of choosing 3 consonants from 17 consonants)

= (5C2) × (17C3)

By using the formula,

nCr = $$\dfrac{ n!}{r!(n – r)!}$$

= 10 × (17×8×5)

= 10 × 680

= 6800

Now we need to find the no. of words that can be formed by 2 vowels and 3 consonants.

The arrangement is similar 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 words that can be formed containing 2 vowels and 3 consonants are 816000.

Answered by Sakshi | 1 year ago

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