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How many 4 number combinations are their using numbers 0-9?

Marijustin

Lvl 1
2010-10-12 14:35:22

Of the 10,000 4-digit numbers 5040 are non-repeating, 4320 one-repeating (doubles), 270 two-repeating (dual-doubles), 360 one-tripled, and 10 quadruples. Since a non-repeating number has 23 more siblings, we can divide 5040 by 24 to obtain 210 distinct non-repeating-digit numbers which are listed below.

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4-digit, non-repeating-digit combinations (24-way)0123, 0124, 0125, 0126, 0127, 0128, 0129, 0134, 0135, 0136, 0137, 0138, 0139, 0145, 0146, 0147, 0148, 0149, 0156, 0157, 0158, 0159, 0167, 0168, 0169, 0178, 0179, 0189, 0234, 0235, 0236, 0237, 0238, 0239, 0245, 0246, 0247, 0248, 0249, 0256, 0257, 0258, 0259, 0267, 0268, 0269, 0278, 0279, 0289, 0345, 0346, 0347, 0348, 0349, 0356, 0357, 0358, 0359, 0367, 0368, 0369, 0378, 0379, 0389, 0456, 0457, 0458, 0459, 0467, 0468, 0469, 0478, 0479, 0489, 0567, 0568, 0569, 0578, 0579, 0589, 0678, 0679, 0689, 0789, 1234, 1235, 1236, 1237, 1238, 1239, 1245, 1246, 1247, 1248, 1249, 1256, 1257, 1258, 1259, 1267, 1268, 1269, 1278, 1279, 1289, 1345, 1346, 1347, 1348, 1349, 1356, 1357, 1358, 1359, 1367, 1368, 1369, 1378, 1379, 1389, 1456, 1457, 1458, 1459, 1467, 1468, 1469, 1478, 1479, 1489, 1567, 1568, 1569, 1578, 1579, 1589, 1678, 1679, 1689, 1789, 2345, 2346, 2347, 2348, 2349, 2356, 2357, 2358, 2359, 2367, 2368, 2369, 2378, 2379, 2389, 2456, 2457, 2458, 2459, 2467, 2468, 2469, 2478, 2479, 2489, 2567, 2568, 2569, 2578, 2579, 2589, 2678, 2679, 2689, 2789, 3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689, 3789, 4567, 4568, 4569, 4578, 4579, 4589, 4678, 4679, 4689, 4789, 5678, 5679, 5689, 5789, 6789

Similarly, since twelve one-repeating numbers can be represented by one number, there are 4320/12=360 distinct one-repeating-digit numbers (doubles) as listed below.

4-digit, one-repeating-digit (doubles) combinations (12-way)0012, 0013, 0014, 0015, 0016, 0017, 0018, 0019, 0023, 0024, 0025, 0026, 0027, 0028, 0029, 0034, 0035, 0036, 0037, 0038, 0039, 0045, 0046, 0047, 0048, 0049, 0056, 0057, 0058, 0059, 0067, 0068, 0069, 0078, 0079, 0089, 0112, 0113, 0114, 0115, 0116, 0117, 0118, 0119, 0122, 0133, 0144, 0155, 0166, 0177, 0188, 0199, 0223, 0224, 0225, 0226, 0227, 0228, 0229, 0233, 0244, 0255, 0266, 0277, 0288, 0299, 0334, 0335, 0336, 0337, 0338, 0339, 0344, 0355, 0366, 0377, 0388, 0399, 0445, 0446, 0447, 0448, 0449, 0455, 0466, 0477, 0488, 0499, 0556, 0557, 0558, 0559, 0566, 0577, 0588, 0599, 0667, 0668, 0669, 0677, 0688, 0699, 0778, 0779, 0788, 0799, 0889, 0899, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1134, 1135, 1136, 1137, 1138, 1139, 1145, 1146, 1147, 1148, 1149, 1156, 1157, 1158, 1159, 1167, 1168, 1169, 1178, 1179, 1189, 1223, 1224, 1225, 1226, 1227, 1228, 1229, 1233, 1244, 1255, 1266, 1277, 1288, 1299, 1334, 1335, 1336, 1337, 1338, 1339, 1344, 1355, 1366, 1377, 1388, 1399, 1445, 1446, 1447, 1448, 1449, 1455, 1466, 1477, 1488, 1499, 1556, 1557, 1558, 1559, 1566, 1577, 1588, 1599, 1667, 1668, 1669, 1677, 1688, 1699, 1778, 1779, 1788, 1799, 1889, 1899, 2234, 2235, 2236, 2237, 2238, 2239, 2245, 2246, 2247, 2248, 2249, 2256, 2257, 2258, 2259, 2267, 2268, 2269, 2278, 2279, 2289, 2334, 2335, 2336, 2337, 2338, 2339, 2344, 2355, 2366, 2377, 2388, 2399, 2445, 2446, 2447, 2448, 2449, 2455, 2466, 2477, 2488, 2499, 2556, 2557, 2558, 2559, 2566, 2577, 2588, 2599, 2667, 2668, 2669, 2677, 2688, 2699, 2778, 2779, 2788, 2799, 2889, 2899, 3345, 3346, 3347, 3348, 3349, 3356, 3357, 3358, 3359, 3367, 3368, 3369, 3378, 3379, 3389, 3445, 3446, 3447, 3448, 3449, 3455, 3466, 3477, 3488, 3499, 3556, 3557, 3558, 3559, 3566, 3577, 3588, 3599, 3667, 3668, 3669, 3677, 3688, 3699, 3778, 3779, 3788, 3799, 3889, 3899, 4456, 4457, 4458, 4459, 4467, 4468, 4469, 4478, 4479, 4489, 4556, 4557, 4558, 4559, 4566, 4577, 4588, 4599, 4667, 4668, 4669, 4677, 4688, 4699, 4778, 4779, 4788, 4799, 4889, 4899, 5567, 5568, 5569, 5578, 5579, 5589, 5667, 5668, 5669, 5677, 5688, 5699, 5778, 5779, 5788, 5799, 5889, 5899, 6678, 6679, 6689, 6778, 6779, 6788, 6799, 6889, 6899, 7789, 7889, 7899

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Again, since six dual-doubles numbers can be represented by one number, there are 270/6=45 distinct dual-double-digit numbers as listed below.

4-digit, dual-double-digit combinations (6-way)0011, 0022, 0033, 0044, 0055, 0066, 0077, 0088, 0099, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2233, 2244, 2255, 2266, 2277, 2288, 2299, 3344, 3355, 3366, 3377, 3388, 3399, 4455, 4466, 4477, 4488, 4499, 5566, 5577, 5588, 5599, 6677, 6688, 6699, 7788, 7799, 8899

Finally, since four dual-doubles numbers can be represented by one number, there are 360/4=90 distinct one-tripled-digit numbers as listed below.

4-digit, one-tripled-digit combinations (4-way)0001, 0002, 0003, 0004, 0005, 0006, 0007, 0008, 0009, 0111, 0222, 0333, 0444, 0555, 0666, 0777, 0888, 0999, 1112, 1113, 1114, 1115, 1116, 1117, 1118, 1119, 1222, 1333, 1444, 1555, 1666, 1777, 1888, 1999, 2223, 2224, 2225, 2226, 2227, 2228, 2229, 2333, 2444, 2555, 2666, 2777, 2888, 2999, 3334, 3335, 3336, 3337, 3338, 3339, 3444, 3555, 3666, 3777, 3888, 3999, 4445, 4446, 4447, 4448, 4449, 4555, 4666, 4777, 4888, 4999, 5556, 5557, 5558, 5559, 5666, 5777, 5888, 5999, 6667, 6668, 6669, 6777, 6888, 6999, 7778, 7779, 7888, 7999, 8889, 8999

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The following table and figures summarize the foregoing facts and the probability of winning with 4-digit boxes.Group name and aliasesHow many 4-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 goupNon-repeating (24-way)50402101:41750.40%One-repeating (12-way) (Doubles)43203601:83343.20%Two-repeating (6-way) (Dual-Doubles)270451:16672.70%One-tripled (4-way) (triples)360901:25003.60%Quadruples10101:10,0000.1%

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2010-10-12 14:35:22
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Q: How many 4 number combinations are their using numbers 0-9?
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