Question

Three digit numbers are formed using the digits $0$, $2$, $4$, $6$ and $8$. $A$ number is chosen at random out of these numbers. What is the probability that this number has the same digits?

• A. $\frac{1}{16}$
• B. $\frac{16}{25}$
• C. $\frac{1}{645}$
• D. $\frac{1}{25}$

Answer 1

Answer: (D)

Since a $3$ -digit number cannot start with digit $0$, the hundredth place can have any of the $4$ digits. Now, the tens and units place can have all the $5$ digits. Therefore, the total possible $3$ -digit numbers are $4 \times 5 \times 5$, i.e., $100$.
The total possible $3$ digit numbers having all digits same $= 4$
Hence, $P$($3$-digit number with same digits) $= \frac{4}{100} = \frac{1}{25}$.