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(D) The word $DAUGHTER$ contains $8$ distinct letters: $D, A, U, G, H, T, E, R$. There are $3$ vowels $(A, U, E)$ and $5$ consonants $(D, G, H, T, R)$

Vedclass · Accepted Answer

$3600$

Vedclass · Answer

(D) The word $DAUGHTER$ contains $8$ distinct letters: $D, A, U, G, H, T, E, R$. There are $3$ vowels $(A, U, E)$ and $5$ consonants $(D, G, H, T, R)$. We need to select $2$ vowels out of $3$ and $3$ consonants out of $5$. The number of ways to select the letters is $^3C_2 	imes ^5C_3 = 3 	imes 10 = 30$. Each selection consists of $5$ letters,which can be arranged among themselves in $5!$ ways. $5! = 120$. Therefore,the total number of words that can be formed is $30 	imes 120 = 3600$.

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

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