Of the number formed by using all the figures 1,2,3,4,5 only once ,how many are even?

To determine how many numbers formed by using all the digits 1, 2, 3, 4, and 5 exactly once are even, follow these steps:

### Step-by-Step Solution:

1. **Identify the Requirement for the Number to be Even:**
   - A number is even if its last digit is an even digit.
   - From the digits 1, 2, 3, 4, and 5, the even digits are 2 and 4.

2. **Calculate the Number of Permutations for Each Even Digit as the Last Digit:**

   - **Case 1: Last digit is 2**
     - Remaining digits: 1, 3, 4, 5
     - Number of permutations of the remaining 4 digits = \(4!\)
     - \(4! = 4 \times 3 \times 2 \times 1 = 24\)

   - **Case 2: Last digit is 4**
     - Remaining digits: 1, 2, 3, 5
     - Number of permutations of the remaining 4 digits = \(4!\)
     - \(4! = 4 \times 3 \times 2 \times 1 = 24\)

3. **Add the Number of Permutations for Both Cases:**
   - Total number of even numbers = \(24 + 24 = 48\)

### Conclusion:
There are \(48\) numbers that can be formed using the digits 1, 2, 3, 4, and 5 exactly once where the number is even.

Would you like more details or have any questions?

Here are 5 additional questions you might consider:
1. How many odd numbers can be formed using the digits 1, 2, 3, 4, and 5 exactly once?
2. How many numbers can be formed using the digits 1, 2, 3, 4, and 5 exactly once that are divisible by 5?
3. How many 4-digit numbers can be formed using the digits 1, 2, 3, and 4 exactly once that are divisible by 4?
4. How many numbers can be formed using the digits 1, 2, 3, and 4 exactly once that are multiples of 3?
5. How many 3-digit even numbers can be formed using the digits 1, 2, 3, and 4 exactly once?

**Tip:** When determining the number of possible permutations that satisfy certain conditions, consider fixing the digit(s) that meet the condition and then permuting the remaining digits.

Discover how many even numbers can be formed using the digits 1, 2, 3, 4, and 5 exactly once with a step-by-step solution. This problem involves permutations and determining even digits. Suitable for students in Grades 7-9.

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