Question

The probability of forming a three-digit numbers with the same digits, when three-digit numbers are formed out of the digits $0,2,4,6,8$ is

• A. $\frac{1}{16}$
• B. $\frac{1}{12}$
• C. $\frac{1}{645}$
• D. $\frac{1}{25}$

Answer 1

The correct option is D

$\frac{1}{25}$

Explanation for the correct option :

Given digits are $0,2,4,6,8$

To form a $3$ digit number $0$ cannot be in a hundred place.

So, the number of choice remain is $4$.

For tenth and unit place each place has $5$ choice.
So, the total number of $3$ digit numbers formed by the given digits are,$=4\times 5\times 5=100$

The three-digit numbers formed using given digits that have the same digits are $222,444,666$ and $888$
Now, the required probability,

$$\begin{gathered} =\frac{\mathrm{Number}\mathrm{of}\mathrm{three}\mathrm{digit}\mathrm{numbers}\mathrm{formed}\mathrm{having}\mathrm{same}\mathrm{digits}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{three}\mathrm{digit}\mathrm{numbers}\mathrm{formed}\mathrm{using}\mathrm{the}\mathrm{given}\mathrm{digits}} \\ =\frac{4}{100} \\ =\frac{1}{25} \end{gathered}$$

Therefore, the probability of forming a three-digit number is $${\displaystyle \frac{1}{25}}$$

Hence, option D is the correct answer.