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)

Out of $7$ consonants, the number of ways of selecting $3$ consonants $={}^7{C}_3$
Similarly, number of ways of selecting
$2$ vowels out of $4$ vowels $={}^4{C}_2$
$\therefore$ Total number of words formed
$={}^7{C}_3\times {}^4{C}_2\times {}^5{P}_5$
$=\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{4\times 3}{2\times 1}\times 5!$
$=7\times 5\times 2\times 3\times 120=25200$