From 5 consonants and 5 vowels,how many words | vedclass

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(A) We need to form words using $3$ consonants and $2$ vowels from $5$ consonants and $5$ vowels.First,we select the consonants and vowels:Number of w

Vedclass · Accepted Answer

$12000$

Vedclass · Answer

(A) We need to form words using $3$ consonants and $2$ vowels from $5$ consonants and $5$ vowels.First,we select the consonants and vowels:Number of ways to select $3$ consonants from $5$ is ${}^5C_3 = \frac{5 	imes 4}{2 	imes 1} = 10$.Number of ways to select $2$ vowels from $5$ is ${}^5C_2 = \frac{5 	imes 4}{2 	imes 1} = 10$.Total ways to select the letters = $10 	imes 10 = 100$.Now,these $5$ selected letters can be arranged among themselves in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Total number of words formed = $100 	imes 120 = 12000$.

From $5$ consonants and $5$ vowels,how many words can be formed using $3$ consonants and $2$ vowels?

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