How many words can be formed by taking 3 cons | vedclass

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Question

(D) Step $1$: Select $3$ consonants from $5$ available consonants,which can be done in $^5C_3$ ways.Step $2$: Select $2$ vowels from $4$ available vow

Vedclass · Accepted Answer

$(^5C_3 	imes ^4C_2) 	imes 5!$

Vedclass · Answer

(D) Step $1$: Select $3$ consonants from $5$ available consonants,which can be done in $^5C_3$ ways.Step $2$: Select $2$ vowels from $4$ available vowels,which can be done in $^4C_2$ ways.Step $3$: The total number of ways to select the letters is $^5C_3 	imes ^4C_2$.Step $4$: Since we have selected $5$ letters in total ($3$ consonants + $2$ vowels),these $5$ letters can be arranged among themselves in $5!$ ways.Step $5$: Therefore,the total number of words that can be formed is $(^5C_3 	imes ^4C_2) 	imes 5!$.

How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels?

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