Question

Out of $7$ consonants and $4$ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2$ vowels, is

• A. $24800$
• B. $25100$
• C. $25200$
• D. $25400$

Answer 1

Answer: (C)

$25200$

Answer 2

Reqd. number of ways $=\,^{7}C_{3}\times\,^{4}C_{2}\times 5!\,\, \frac{7\times6\times5}{1\times2\times3}\times\frac{4\times3}{1\times2}\times120$ $=35\times6\times 120$ $=210\times120$