Question

A $3-digit$ code is made up of three different digits from the set $\{2,3,4,5,6\}$. If $4$ is always the first digit in the code, calculate the total number of $3$-digit codes can be formed using each digit only once.

• A. $3$
• B. $5$
• C. $12$
• D. $13$
• E. $20$

Answer 1

Answer: (C)

$12$

Since, we have given set of digits $2,3,4,5,6$

For hundred's place of 3-digit code only one digit i.e $"4"$ digit is fixed.

Now we left with four digits.

$\therefore$ For ten's place of 3-digit code we have $4$ digits. Again we left with only $3$ digits because each digit is used only once.

$\therefore$ For one's place we can use $3$ digits.

So, total number of 3-digit codes can be formed with given $5$ digits $=1\times 4\times 3=12$

Option C is correct.