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# How many 3 digit combinations can be made from 0 to 9 digits?

Wiki User

2013-10-11 05:14:47

Assuming the digits can be used again, there are 10*10*10 or 1000 three digit combinations.

Of the 1000 3-digit numbers 720 are non-repeating, 270 one-repeating, and 10 triples. Since a non-repeating number has 5 more siblings, we can divide 720 by 6 to obtain 120 distinct non-repeating-digit numbers which are listed below.

3-digit, non-repeating combinations (6-way)012, 013, 014, 015, 016, 017, 018, 019, 023, 024, 025, 026, 027, 028, 029, 034, 035, 036, 037, 038, 039, 045, 046, 047, 048, 049, 056, 057, 058, 059, 067, 068, 069, 078, 079, 089, 123, 124, 125, 126, 127, 128, 129, 134, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 156, 157, 158, 159, 167, 168, 169, 178, 179, 189, 234, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 256, 257, 258, 259, 267, 268, 269, 278, 279, 289, 345, 346, 347, 348, 349, 356, 357, 358, 359, 367, 368, 369, 378, 379, 389, 456, 457, 458, 459, 467, 468, 469, 478, 479, 489, 567, 568, 569, 578, 579, 589, 678, 679, 689, 789

Similarly, since three one-repeating numbers can be represented by one number, there are 270/3=90 distinct one-repeating numbers (doubles) as listed below.

3-digit, one-repeating combinations (Doubles) (3-way)001, 002, 003, 004, 005, 006, 007, 008, 009, 011, 022, 033, 044, 055, 066, 077, 088, 099, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 334, 335, 336, 337, 338, 339, 344, 355, 366, 377, 388, 399, 445, 446, 447, 448, 449, 455, 466, 477, 488, 499, 556, 557, 558, 559, 566, 577, 588, 599, 667, 668, 669, 677, 688, 699, 778, 779, 788, 799, 889, 899

The following table and figures summarize the foregoing facts and the probability of winning with any order arrangement of 3-digit games.Group name and aliasesHow many 3-dig Numbers fall into this groupHow many distinct members of the groupodds of winning with a number in the groupProbability of a number drawn to be in the groupNon-repeat (6-way)7201201:16772%One-repeat (3-way) (Doubles)270901:33327%Triples10101:10001%
One thousand if you allow repeating digits.

Wiki User

2013-10-11 05:14:47
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