Question

Out of $7$ consonants and $4$ vowels, the number of words that can be formed out of $3$ consonants and $2$ vowels is:

• A. $462$
• B. $2800$
• C. $25200$
• D. $24540$

Answer 1

Answer: (C)

$25200$

Number of ways of selecting ($3$ consonants out of $7$) and ($2$ vowels out of $4$) $={}^7{C}_3\times {}^4{C}_2=210$

Now the word formed from $3$ consonants and $2$ vowels is a $5$ letter word.

The letters of the word can be rearranged in $5!$ ways

Hence the number of words $=210\times 5!=25200$