Question

Out of $7$ consonants and $4$ vowels, words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is

• A. $210$
• B. $25200$
• C. $2520$
• D. $302400$

Answer 1

Answer: (B)

$25200$

Total no. of consonants is $7$ and of vowels is $4$

Out of $7$ consonants, $3$ are chosen to form a word. So, this can be done in ${}^7{C}_3$ ways

Out of $4$ vowels, $2$ are chosen to form a word. So, that can be done in ${}^4{C}_2$ ways

So, the no. of select $3$ consonants and $2$ vowels is ${}^7{C}_3{\times }^4{C}_2$

Now, we can arrange the word containing $5$ letters in $5!$ ways.

Thus, the total no. of words formed each having $3$ consonants and $2$ vowels is

${}^7{C}_3{\times }^4{C}_2\times 5!=25200$

Hence, the answer is $25200$.