SOLUTION: how many three-digit numbers greater than 600 can be performed by using the digits 4,5,6,7,8

We can choose the first digit any of these 3 ways: {6,7,8}

For each of those 3 ways we can choose the first digit,
we can then choose the second digit any of these 5 ways {4,5,6,7,8}
That's 3×5 or 15 ways to chose the first and second digits.

For each of those 15 ways we can choose the first and second digits,
we can then choose the third digit any of these 5 ways {4,5,6,7,8}
That's 15×5 or 75 ways to chose the first, second, and third digits,
so that's the answer.

Answer: 75

Here are all 75 three digit numbers:
 1. 644   2. 645   3. 646   4. 647   5. 648   6. 654   7. 655   8. 656   9. 657  10. 658
11. 664  12. 665  13. 666  14. 667  15. 668  16. 674  17. 675  18. 676  19. 677  20. 678
21. 684  22. 685  23. 686  24. 687  25. 688  26. 744  27. 745  28. 746  29. 747  30. 748
31. 754  32. 755  33. 756  34. 757  35. 758  36. 764  37. 765  38. 766  39. 767  40. 768
41. 774  42. 775  43. 776  44. 777  45. 778  46. 784  47. 785  48. 786  49. 787  50. 788
51. 844  52. 845  53. 846  54. 847  55. 848  56. 854  57. 855  58. 856  59. 857  60. 858
61. 864  62. 865  63. 866  64. 867  65. 868  66. 874  67. 875  68. 876  69. 877  70. 878
71. 884  72. 885  73. 886  74. 887  75. 888

Edwin