Question

用0到9这10个数字可以组成多少个没有重复数字的三位数？(要有简单的算式过程）

Answer 1

这里有个问题，就是数字的首位数可不可以是0？虽然说首位的0常常是省略掉的，但是写的话也不能算错，所以还是你自己来判断吧。结论是：如果首位不允许为0，那么共有60种，如果首位可以为0，那么共有228种。所有解都列在下面：

1 + 42 + 695 = 0738
1 + 43 + 685 = 0729
1 + 45 + 683 = 0729
1 + 45 + 692 = 0738
1 + 52 + 793 = 0846
1 + 53 + 792 = 0846
1 + 72 + 386 = 0459
1 + 72 + 395 = 0468
1 + 75 + 392 = 0468
1 + 76 + 382 = 0459
1 + 82 + 376 = 0459
1 + 82 + 493 = 0576
1 + 83 + 492 = 0576
1 + 83 + 645 = 0729
1 + 85 + 643 = 0729
1 + 86 + 372 = 0459
1 + 92 + 375 = 0468
1 + 92 + 483 = 0576
1 + 92 + 645 = 0738
1 + 92 + 753 = 0846
1 + 93 + 482 = 0576
1 + 93 + 752 = 0846
1 + 95 + 372 = 0468
1 + 95 + 642 = 0738
2 + 41 + 695 = 0738
2 + 45 + 691 = 0738
2 + 46 + 987 = 1035
2 + 47 + 986 = 1035
2 + 51 + 793 = 0846
2 + 53 + 764 = 0819
2 + 53 + 791 = 0846
2 + 54 + 763 = 0819
2 + 63 + 754 = 0819
2 + 64 + 753 = 0819
2 + 64 + 987 = 1053
2 + 67 + 984 = 1053
2 + 71 + 386 = 0459
2 + 71 + 395 = 0468
2 + 75 + 391 = 0468
2 + 76 + 381 = 0459
2 + 81 + 376 = 0459
2 + 81 + 493 = 0576
2 + 83 + 491 = 0576
2 + 84 + 967 = 1053
2 + 86 + 371 = 0459
2 + 86 + 947 = 1035
2 + 87 + 946 = 1035
2 + 87 + 964 = 1053
2 + 91 + 375 = 0468
2 + 91 + 483 = 0576
2 + 91 + 645 = 0738
2 + 91 + 753 = 0846
2 + 93 + 481 = 0576
2 + 93 + 751 = 0846
2 + 95 + 371 = 0468
2 + 95 + 641 = 0738
3 + 41 + 685 = 0729
3 + 45 + 681 = 0729
3 + 45 + 978 = 1026
3 + 48 + 975 = 1026
3 + 51 + 792 = 0846
3 + 52 + 764 = 0819
3 + 52 + 791 = 0846
3 + 54 + 762 = 0819
3 + 62 + 754 = 0819
3 + 64 + 752 = 0819
3 + 74 + 985 = 1062
3 + 75 + 948 = 1026
3 + 75 + 984 = 1062
3 + 78 + 945 = 1026
3 + 81 + 492 = 0576
3 + 81 + 645 = 0729
3 + 82 + 491 = 0576
3 + 84 + 975 = 1062
3 + 85 + 641 = 0729
3 + 85 + 974 = 1062
3 + 91 + 482 = 0576
3 + 91 + 752 = 0846
3 + 92 + 481 = 0576
3 + 92 + 751 = 0846
4 + 35 + 987 = 1026
4 + 37 + 985 = 1026
4 + 38 + 579 = 0621
4 + 39 + 578 = 0621
4 + 52 + 763 = 0819
4 + 53 + 762 = 0819
4 + 62 + 753 = 0819
4 + 62 + 987 = 1053
4 + 63 + 752 = 0819
4 + 67 + 982 = 1053
4 + 68 + 279 = 0351
4 + 69 + 278 = 0351
4 + 73 + 985 = 1062
4 + 75 + 983 = 1062
4 + 78 + 269 = 0351
4 + 78 + 539 = 0621
4 + 79 + 268 = 0351
4 + 79 + 538 = 0621
4 + 82 + 967 = 1053
4 + 83 + 975 = 1062
4 + 85 + 937 = 1026
4 + 85 + 973 = 1062
4 + 87 + 935 = 1026
4 + 87 + 962 = 1053
5 + 34 + 987 = 1026
5 + 37 + 984 = 1026
5 + 41 + 683 = 0729
5 + 41 + 692 = 0738
5 + 42 + 691 = 0738
5 + 43 + 681 = 0729
5 + 43 + 978 = 1026
5 + 48 + 973 = 1026
5 + 71 + 392 = 0468
5 + 72 + 391 = 0468
5 + 73 + 948 = 1026
5 + 73 + 984 = 1062
5 + 74 + 983 = 1062
5 + 78 + 943 = 1026
5 + 81 + 643 = 0729
5 + 83 + 641 = 0729
5 + 83 + 974 = 1062
5 + 84 + 937 = 1026
5 + 84 + 973 = 1062
5 + 87 + 934 = 1026
5 + 91 + 372 = 0468
5 + 91 + 642 = 0738
5 + 92 + 371 = 0468
5 + 92 + 641 = 0738
6 + 27 + 498 = 0531
6 + 28 + 479 = 0513
6 + 28 + 497 = 0531
6 + 29 + 478 = 0513
6 + 42 + 987 = 1035
6 + 47 + 298 = 0351
6 + 47 + 982 = 1035
6 + 48 + 297 = 0351
6 + 58 + 179 = 0243
6 + 59 + 178 = 0243
6 + 71 + 382 = 0459
6 + 72 + 381 = 0459
6 + 78 + 159 = 0243
6 + 78 + 429 = 0513
6 + 79 + 158 = 0243
6 + 79 + 428 = 0513
6 + 81 + 372 = 0459
6 + 82 + 371 = 0459
6 + 82 + 947 = 1035
6 + 87 + 942 = 1035
6 + 97 + 248 = 0351
6 + 97 + 428 = 0531
6 + 98 + 247 = 0351
6 + 98 + 427 = 0531
7 + 26 + 498 = 0531
7 + 28 + 496 = 0531
7 + 34 + 985 = 1026
7 + 35 + 984 = 1026
7 + 42 + 986 = 1035
7 + 46 + 298 = 0351
7 + 46 + 982 = 1035
7 + 48 + 296 = 0351
7 + 58 + 169 = 0234
7 + 59 + 168 = 0234
7 + 62 + 984 = 1053
7 + 64 + 982 = 1053
7 + 68 + 159 = 0234
7 + 69 + 158 = 0234
7 + 82 + 946 = 1035
7 + 82 + 964 = 1053
7 + 84 + 935 = 1026
7 + 84 + 962 = 1053
7 + 85 + 934 = 1026
7 + 86 + 942 = 1035
7 + 96 + 248 = 0351
7 + 96 + 428 = 0531
7 + 98 + 246 = 0351
7 + 98 + 426 = 0531
8 + 26 + 479 = 0513
8 + 26 + 497 = 0531
8 + 27 + 496 = 0531
8 + 29 + 476 = 0513
8 + 34 + 579 = 0621
8 + 39 + 574 = 0621
8 + 43 + 975 = 1026
8 + 45 + 973 = 1026
8 + 46 + 297 = 0351
8 + 47 + 296 = 0351
8 + 56 + 179 = 0243
8 + 57 + 169 = 0234
8 + 59 + 167 = 0234
8 + 59 + 176 = 0243
8 + 64 + 279 = 0351
8 + 67 + 159 = 0234
8 + 69 + 157 = 0234
8 + 69 + 274 = 0351
8 + 73 + 945 = 1026
8 + 74 + 269 = 0351
8 + 74 + 539 = 0621
8 + 75 + 943 = 1026
8 + 76 + 159 = 0243
8 + 76 + 429 = 0513
8 + 79 + 156 = 0243
8 + 79 + 264 = 0351
8 + 79 + 426 = 0513
8 + 79 + 534 = 0621
8 + 96 + 247 = 0351
8 + 96 + 427 = 0531
8 + 97 + 246 = 0351
8 + 97 + 426 = 0531
9 + 26 + 478 = 0513
9 + 28 + 476 = 0513
9 + 34 + 578 = 0621
9 + 38 + 574 = 0621
9 + 56 + 178 = 0243
9 + 57 + 168 = 0234
9 + 58 + 167 = 0234
9 + 58 + 176 = 0243
9 + 64 + 278 = 0351
9 + 67 + 158 = 0234
9 + 68 + 157 = 0234
9 + 68 + 274 = 0351
9 + 74 + 268 = 0351
9 + 74 + 538 = 0621
9 + 76 + 158 = 0243
9 + 76 + 428 = 0513
9 + 78 + 156 = 0243
9 + 78 + 264 = 0351
9 + 78 + 426 = 0513
9 + 78 + 534 = 0621

Answer 2

百位的选择有9种，选完百位后，十位的选择有9种，个位的选择有8种，所以共有9*9*8=648种