Using the digits 1,2,3,4,5 to create a 4 digit number sequence by combining the last two digits at the end of the sequence, example...1, 2, 3, 45 or 2, 3,4, 51 or 4, 5, 1, 23 or 4, 5, 1, 32.list all possible combinations in order

Let's solve the problem by listing all possible 4-digit sequences, using the digits 1, 2, 3, 4, and 5, where the last two digits are combined to form a two-digit number. 

### The rule:
- We are forming a 4-digit number, but the last two digits must be combined to create a two-digit number.
- We cannot repeat digits, and each of the digits (1, 2, 3, 4, 5) should appear only once.

We will go systematically and list all the possible combinations.

### Combinations:
1. 1, 2, 3, 45
2. 1, 2, 4, 35
3. 1, 2, 5, 34
4. 1, 3, 2, 45
5. 1, 3, 4, 25
6. 1, 3, 5, 24
7. 1, 4, 2, 35
8. 1, 4, 3, 25
9. 1, 4, 5, 23
10. 1, 5, 2, 34
11. 1, 5, 3, 24
12. 1, 5, 4, 23

13. 2, 1, 3, 45
14. 2, 1, 4, 35
15. 2, 1, 5, 34
16. 2, 3, 1, 45
17. 2, 3, 4, 15
18. 2, 3, 5, 14
19. 2, 4, 1, 35
20. 2, 4, 3, 15
21. 2, 4, 5, 13
22. 2, 5, 1, 34
23. 2, 5, 3, 14
24. 2, 5, 4, 13

25. 3, 1, 2, 45
26. 3, 1, 4, 25
27. 3, 1, 5, 24
28. 3, 2, 1, 45
29. 3, 2, 4, 15
30. 3, 2, 5, 14
31. 3, 4, 1, 25
32. 3, 4, 2, 15
33. 3, 4, 5, 12
34. 3, 5, 1, 24
35. 3, 5, 2, 14
36. 3, 5, 4, 12

37. 4, 1, 2, 35
38. 4, 1, 3, 25
39. 4, 1, 5, 23
40. 4, 2, 1, 35
41. 4, 2, 3, 15
42. 4, 2, 5, 13
43. 4, 3, 1, 25
44. 4, 3, 2, 15
45. 4, 3, 5, 12
46. 4, 5, 1, 23
47. 4, 5, 2, 13
48. 4, 5, 3, 12

49. 5, 1, 2, 34
50. 5, 1, 3, 24
51. 5, 1, 4, 23
52. 5, 2, 1, 34
53. 5, 2, 3, 14
54. 5, 2, 4, 13
55. 5, 3, 1, 24
56. 5, 3, 2, 14
57. 5, 3, 4, 12
58. 5, 4, 1, 23
59. 5, 4, 2, 13
60. 5, 4, 3, 12

### Total Combinations: 60

Would you like further explanations on any part? 

Here are 5 related questions for exploration:
1. How would the result change if digits could be repeated?
2. What happens if the two-digit number cannot start with a 0?
3. How many possible combinations would there be if we used 6 digits instead of 5?
4. How would the list change if we were limited to odd numbers only?
5. Can this type of combination system be generalized to larger sets of numbers?

**Tip:** To organize possible combinations systematically, always vary the first digit first, then the second, and so on to avoid missing any possibilities.

Using the digits 1, 2, 3, 4, 5 to create a 4-digit number sequence by combining the last two digits at the end of the sequence, example...1, 2, 3, 45 or 2, 3, 4, 51 or 4, 5, 1, 23 or 4, 5, 1, 32. List all possible combinations in order.

Discover how to create and list all possible 4-digit combinations using the digits 1, 2, 3, 4, and 5, where the last two digits are combined into a two-digit number. Learn about permutations and the fundamental principle of counting. Suitable for students in Grades 6-8.

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