Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining two of the digits in the middle of the sequence, beginning with the third digits in the sequence, example;   1, 2,34, 5 or 2, 3,4, 51 or 4, 5, 1, 23...list all possible combinations in order

To create a 4-digit sequence using the digits 1, 2, 3, 4, 5 with two of the digits combined in the middle (starting with the third digit), the following steps can be taken:

1. Choose the third digit.
2. Combine the fourth and fifth digits to create a two-digit number.
3. Use the remaining digits for the first and second positions.

Let’s list all possible combinations systematically:

### Combinations with Third Digit as 1
- 2, 3, **14**, 5
- 2, 4, **15**, 3
- 2, 5, **13**, 4
- 3, 2, **14**, 5
- 3, 4, **15**, 2
- 3, 5, **12**, 4
- 4, 2, **13**, 5
- 4, 3, **15**, 2
- 4, 5, **12**, 3
- 5, 2, **13**, 4
- 5, 3, **14**, 2
- 5, 4, **12**, 3

### Combinations with Third Digit as 2
- 1, 3, **24**, 5
- 1, 4, **25**, 3
- 1, 5, **23**, 4
- 3, 1, **24**, 5
- 3, 4, **25**, 1
- 3, 5, **21**, 4
- 4, 1, **23**, 5
- 4, 3, **25**, 1
- 4, 5, **21**, 3
- 5, 1, **23**, 4
- 5, 3, **24**, 1
- 5, 4, **21**, 3

### Combinations with Third Digit as 3
- 1, 2, **34**, 5
- 1, 4, **35**, 2
- 1, 5, **32**, 4
- 2, 1, **34**, 5
- 2, 4, **35**, 1
- 2, 5, **31**, 4
- 4, 1, **35**, 2
- 4, 2, **35**, 1
- 4, 5, **31**, 2
- 5, 1, **32**, 4
- 5, 2, **34**, 1
- 5, 4, **31**, 2

### Combinations with Third Digit as 4
- 1, 2, **45**, 3
- 1, 3, **42**, 5
- 1, 5, **43**, 2
- 2, 1, **45**, 3
- 2, 3, **42**, 1
- 2, 5, **41**, 3
- 3, 1, **45**, 2
- 3, 2, **41**, 5
- 3, 5, **42**, 1
- 5, 1, **43**, 2
- 5, 2, **41**, 3
- 5, 3, **42**, 1

### Combinations with Third Digit as 5
- 1, 2, **54**, 3
- 1, 3, **52**, 4
- 1, 4, **53**, 2
- 2, 1, **54**, 3
- 2, 3, **52**, 1
- 2, 4, **51**, 3
- 3, 1, **54**, 2
- 3, 2, **51**, 4
- 3, 4, **52**, 1
- 4, 1, **53**, 2
- 4, 2, **51**, 3
- 4, 3, **52**, 1

This list contains all possible combinations when combining two of the digits in the middle, starting with the third digit in the sequence.

Do you have any questions or need further details? Here are five related questions to consider:

1. What are the total possible combinations of a 4-digit number using all 5 digits without any restrictions?
2. How would the combinations change if repetition of digits was allowed?
3. Can you generate all combinations where the middle digits are always even numbers?
4. What would be the impact on the combinations if the first digit had to be odd?
5. How many combinations are possible if we combine the first two digits instead of the middle digits?

**Tip:** Always start by understanding the constraints of the problem before listing out possibilities—it simplifies the process!

Using the digits 1, 2, 3, 4, 5 to create a 4-digit number sequence by combining two of the digits in the middle of the sequence, beginning with the third digits in the sequence, example: 1, 2,34, 5 or 2, 3,4, 51 or 4, 5, 1, 23...list all possible combinations in order.

Explore all possible 4-digit number sequences combining two digits in the middle, starting with the third digit in the sequence, using the digits 1, 2, 3, 4, 5. This problem focuses on combinatorics and permutations, ideal for students in Grades 8-10.

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