5 digital numbers are formed with 0, 1,2,3,4 find the probability of getting 2, in tens place and 0 in the units

To solve the problem of finding the probability of forming a 5-digit number with specific conditions (2 in the tens place and 0 in the units place), we'll break it down into steps.

### Step 1: Total Number of 5-Digit Numbers
Given that we can use the digits \(0, 1, 2, 3, 4\), let's find the total number of 5-digit numbers that can be formed:

- The first digit (the thousands place) cannot be \(0\) (since it's a 5-digit number), so it has 4 possible choices: \(1, 2, 3, 4\).
- The second digit has 5 possible choices: \(0, 1, 2, 3, 4\).
- The third digit also has 5 possible choices: \(0, 1, 2, 3, 4\).
- The fourth digit also has 5 possible choices: \(0, 1, 2, 3, 4\).
- The fifth digit (the units place) also has 5 possible choices: \(0, 1, 2, 3, 4\).

So, the total number of possible 5-digit numbers is:
\[
4 \times 5 \times 5 \times 5 \times 5 = 2500
\]

### Step 2: Number of Favorable Outcomes
Now, we need to count the favorable outcomes where the number has \(2\) in the tens place and \(0\) in the units place.

- The fifth digit (units place) is fixed as \(0\).
- The fourth digit (tens place) is fixed as \(2\).
- The first digit (thousands place) has 4 possible choices: \(1, 2, 3, 4\).
- The second digit has 5 possible choices: \(0, 1, 2, 3, 4\).
- The third digit also has 5 possible choices: \(0, 1, 2, 3, 4\).

So, the number of favorable outcomes is:
\[
4 \times 5 \times 5 = 100
\]

### Step 3: Calculate the Probability
The probability is given by the ratio of the number of favorable outcomes to the total number of possible outcomes:
\[
\text{Probability} = \frac{100}{2500} = \frac{1}{25}
\]

### Final Answer
The probability of getting \(2\) in the tens place and \(0\) in the units place is \(\boxed{\frac{1}{25}}\).

Would you like to know more details or have any questions?

Here are some related questions:
1. What is the probability of getting the digit \(4\) in the thousands place?
2. How many different 5-digit numbers can be formed if the digits cannot repeat?
3. What is the probability of forming a number with at least one digit as \(3\)?
4. How does the probability change if the digits can repeat, except \(0\) cannot be used?
5. What is the probability that all digits in the number are even?

**Tip:** Always double-check your conditions, such as restrictions on digits, to ensure accuracy when calculating probabilities.

Understand the probability of forming a 5-digit number where the tens place is 2 and the units place is 0. Learn how to calculate probabilities using combinatorial methods and specific digit constraints. Suitable for students in Grades 7-9.

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