Out of 7 consonants and 4 vowels,how many wor | vedclass

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(C) Step $1$: Select $3$ consonants out of $7$. The number of ways is ${}^{7}C_{3} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.Step $2$: S

Vedclass · Accepted Answer

$25200$

Vedclass · Answer

(C) Step $1$: Select $3$ consonants out of $7$. The number of ways is ${}^{7}C_{3} = \frac{7 	imes 6 	imes 5}{3 	imes 2 	imes 1} = 35$.Step $2$: Select $2$ vowels out of $4$. The number of ways is ${}^{4}C_{2} = \frac{4 	imes 3}{2 	imes 1} = 6$.Step $3$: The total number of letters selected is $3 + 2 = 5$. These $5$ letters can be arranged among themselves in $5!$ ways.$5! = 5 	imes 4 	imes 3 	imes 2 	imes 1 = 120$.Step $4$: The total number of words that can be formed is the product of the number of selections and the number of arrangements.Total words $= 35 	imes 6 	imes 120 = 210 	imes 120 = 25200$.

Out of $7$ consonants and $4$ vowels,how many words of $3$ consonants and $2$ vowels can be formed?

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