Question

Three-digit numbers are formed using the digits $0 , 2,4,6,8$. 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) $=\frac{4}{100}=\frac{1}{25}$