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 equal to?

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

Answer 1

The correct option is C

$25200$

Explanation for the correct answer:

Calculating the number of words:

Number of consonants $=7$

Number of vowels $=4$

Number of ways of selecting $3$ consonants from $7$ consonants $={}^{7}C_3$ ways

Number of ways of selecting $2$ vowels from $4$ vowels $={}^{4}C_2$ ways

Selected $5$ letters can be arranged in $5!$ ways so we get different words.

Number of words that can be formed $$\begin{gathered} ={}^{7}C_{3}x{}^{4}C_{2}x5! \\ =\frac{7\times 6\times 5}{3\times 2\times 1}\times \frac{4\times 3}{1\times 2}\times 5\times 4\times 3\times 2\times 1 \end{gathered}$$

$=35x6x120$

$=25200$

Thus, the number of words that can be formed is $25200$

Hence, option (C) is the correct answer.