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)

$25200$

Answer 2

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
$={ }^{7} C_{3} \times{ }^{4} C_{2} \times{ }^{5} P_{5}$
$=\frac{7 \times 6 \times 5}{3 \times 2 \times 1} \times \frac{4 \times 3}{2 \times 1} \times 5 !$
$=7 \times 5 \times 2 \times 3 \times 120=25200$