how many numbers between 2000 and 5000 can be made from the digits 1, 2, 4, 5, 7, and 8 if each digit is used only once?
+26388 how many numbers between 2000 and 5000 can be made
from the digits 1, 2, 4, 5, 7, and 8 if each digit is used only once?
\(\begin{array}{|rcll|} \hline 2xxx &=& \frac{5!}{(5-3)!} = \frac{5!}{2!} = 60 \\ 4xxx &=& \frac{5!}{(5-3)!} = \frac{5!}{2!} = 60 \\ \hline \end{array}\)
1. 2145
2. 2147
3. 2148
4. 2154
5. 2157
6. 2158
7. 2174
8. 2175
9. 2178
10. 2184
11. 2185
12. 2187
13. 2415
14. 2417
15. 2418
16. 2451
17. 2457
18. 2458
19. 2471
20. 2475
21. 2478
22. 2481
23. 2485
24. 2487
25. 2514
26. 2517
27. 2518
28. 2541
29. 2547
30. 2548
31. 2571
32. 2574
33. 2578
34. 2581
35. 2584
36. 2587
37. 2714
38. 2715
39. 2718
40. 2741
41. 2745
42. 2748
43. 2751
44. 2754
45. 2758
46. 2781
47. 2784
48. 2785
49. 2814
50. 2815
51. 2817
52. 2841
53. 2845
54. 2847
55. 2851
56. 2854
57. 2857
58. 2871
59. 2874
60. 2875
61. 4125
62. 4127
63. 4128
64. 4152
65. 4157
66. 4158
67. 4172
68. 4175
69. 4178
70. 4182
71. 4185
72. 4187
73. 4215
74. 4217
75. 4218
76. 4251
77. 4257
78. 4258
79. 4271
80. 4275
81. 4278
82. 4281
83. 4285
84. 4287
85. 4512
86. 4517
87. 4518
88. 4521
89. 4527
90. 4528
91. 4571
92. 4572
93. 4578
94. 4581
95. 4582
96. 4587
97. 4712
98. 4715
99. 4718
100. 4721
101. 4725
102. 4728
103. 4751
104. 4752
105. 4758
106. 4781
107. 4782
108. 4785
109. 4812
110. 4815
111. 4817
112. 4821
113. 4825
114. 4827
115. 4851
116. 4852
117. 4857
118. 4871
119. 4872
120. 4875
120 numbers between 2000 and 5000 can be made.
