form 17 consonant and 5 vowels how many words of 3 consonants and 2 vowels can be made if all the letter are different
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Given:
No. of consonants= 17
No. of vowels = 5
No. of consonants in the required word= 3
No. of vowels in the required word= 2
To find:
No. of words that can be made from 3 consonants and 2 vowels.
Solution:
No. of ways of choosing 3 consonants= 17C3
No. of ways of choosing 2 vowels = 5C2
No. of ways of choosing 3 consonants and 2 vowels= 17C3 * 5C2
No. of ways after arranging the letters amongst themselves= 5! 17C3 * 5C2
=120* 680* 10
= 816,000
Therefore, there are 816,000 words are possible with 3 consonants and 2 vowels.
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