5 digit numbers are formed with 0,1,2,3,4 find the probabillity of getting 2 in the 10s palce and 0 in the units palce

Let's break down the problem step by step to find the probability of forming a 5-digit number with specific digits in certain places.

### Step 1: Understand the Problem
- **Digits Available:** 0, 1, 2, 3, 4
- **Form a 5-digit number:** We need to make a 5-digit number using these digits.
- **Specific Requirement:** The digit '2' must be in the tens place, and the digit '0' must be in the units place.

### Step 2: Determine Total Possible 5-Digit Numbers
For a 5-digit number:
- The first digit (thousands place) cannot be '0' (otherwise it wouldn't be a 5-digit number).
- The remaining digits can be any of the five digits available (0, 1, 2, 3, 4).

So, for the total number of 5-digit combinations:
- **First digit:** Can be 1, 2, 3, or 4 (4 options).
- **Second digit:** Can be any of the 5 digits (0, 1, 2, 3, 4).
- **Third digit:** Can be any of the 5 digits (0, 1, 2, 3, 4).
- **Fourth digit:** Can be any of the 5 digits (0, 1, 2, 3, 4).
- **Fifth digit (units place):** Can be any of the 5 digits (0, 1, 2, 3, 4).

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

### Step 3: Determine Favorable Outcomes
Now, let's consider the specific conditions:
- **2 must be in the tens place:** This fixes the fourth digit as '2'.
- **0 must be in the units place:** This fixes the fifth digit as '0'.

For the remaining three digits (first, second, and third places):
- **First digit:** Can still be 1, 3, or 4 (not 0 or 2 to ensure it's a 5-digit number) → 3 options.
- **Second digit:** Can be any of the 5 digits (0, 1, 2, 3, 4).
- **Third digit:** Can be any of the 5 digits (0, 1, 2, 3, 4).

Thus, the number of favorable outcomes is:
\[ 3 \times 5 \times 5 = 75 \]

### Step 4: Calculate the Probability
The probability of getting a 5-digit number with 2 in the tens place and 0 in the units place is:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{75}{2500} = \frac{3}{100} = 0.03
\]

### Final Answer
The probability is **0.03** or **3%**.

Would you like any further details on this? Here are some related questions you might find interesting:

1. What if we had to place a different digit in the tens place?
2. How would the probability change if we allowed repeating digits?
3. What happens if we use a different set of digits, like 1, 2, 3, 4, 5?
4. How many 5-digit numbers can be formed if no digits repeat?
5. What is the probability of forming a number where '0' is in the hundreds place?

**Tip:** When calculating probabilities, always ensure to count both the total possible outcomes and the favorable outcomes accurately!

Learn how to calculate the probability of forming a 5-digit number where the digit '2' is in the tens place and '0' is in the units place. This problem involves combinatorial analysis and probability calculations. Suitable for students in Grades 9-12.

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