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Combinatorics
Combinations calculation for the Irish Lotto
The combination calculation for the Irish Lotto indicates how many combinations exist in a series of n numbers.
How many pairs are formed with ten numbers?
How many groups of 3 numbers can be formed with 6 numbers?
How many groups of 4, 5 or 6 numbers are there in the Irish Lotto lottery?
This table provides the answers.
NUMBER 1 Num 2 Num 3 Num 4 Num 5 Num 6 Num 7 Num 8 Num 9 Num 10 Num
6 6 15 20 15 6 1
7 7 21 35 35 21 7 1
8 8 28 56 70 56 28 8 1
9 9 36 84 126 126 84 36 9 1
10 10 45 120 210 252 210 120 45 10 1
11 11 55 165 330 462 462 330 165 55 11
12 12 66 220 495 792 924 792 495 220 66
13 13 78 286 715 1.287 1.716 1.716 1.287 715 286
14 14 91 364 1.001 2.002 3.003 3.432 3.003 2.002 1.001
15 15 105 455 1.365 3.003 5.005 6.435 6.435 5.005 3.003
16 16 120 560 1.820 4.368 8.008 11.440 12.870 11.440 8.008
17 17 136 680 2.380 6.188 12.376 19.448 24.310 24.310 19.448
18 18 153 816 3.060 8.568 18.564 31.824 43.758 48.620 43.758
19 19 171 969 3.876 11.628 27.132 50.388 75.582 92.378 92.378
20 20 190 1.140 4.845 15.504 38.760 77.520 125.970 167.960 184.756
21 21 210 1.330 5.985 20.349 54.264 116.280 203.490 293.930 352.716
22 22 231 1.540 7.315 26.334 74.613 170.544 319.770 497.420 646.646
23 23 253 1.771 8.855 33.649 100.947 245.157 490.314 817.190 1.144.066
24 24 276 2.024 10.626 42.504 134.596 346.104 735.471 1.307.504 1.961.256
25 25 300 2.300 12.650 53.130 177.100 480.700 1.081.575 2.042.975 3.268.760
26 26 325 2.600 14.950 65.780 230.230 657.800 1.562.275 3.124.550 5.311.735
27 27 351 2.925 17.550 80.730 296.010 888.030 2.220.075 4.686.825 8.436.285
28 28 378 3.276 20.475 98.280 376.740 1.184.040 3.108.105 6.906.900 13.123.110
29 29 406 3.654 23.751 118.755 475.020 1.560.780 4.292.145 10.015.005 20.030.010
30 30 435 4.060 27.405 142.506 593.775 2.035.800 5.852.925 14.307.150 30.045.015
31 31 465 4.495 31.465 169.911 736.281 2.629.575 7.888.725 20.160.075 44.352.165
32 32 496 4.960 35.960 201.376 906.192 3.365.856 10.518.300 28.048.800 64.512.240
33 33 528 5.456 40.920 237.336 1.107.568 4.272.048 13.884.156 38.567.100 92.561.040
34 34 561 5.984 46.376 278.256 1.344.904 5.379.616 18.156.204 52.451.256 131.128.140
35 35 595 6.545 52.360 324.632 1.623.160 6.724.520 23.535.820 70.607.460 183.579.396
36 36 630 7.140 58.905 376.992 1.947.792 8.347.680 30.260.340 94.143.280 254.186.856
37 37 666 7.770 66.045 435.897 2.324.784 10.295.472 38.608.020 124.403.620 348.330.136
38 38 703 8.436 73.815 501.942 2.760.681 12.620.256 48.903.492 163.011.640 472.733.756
39 39 741 9.139 82.251 575.757 3.262.623 15.380.937 61.523.748 211.915.132 635.745.396
40 40 780 9.880 91.390 658.008 3.838.380 18.643.560 76.904.685 273.438.880 847.660.528
41 41 820 10.660 101.270 749.398 4.496.388 22.481.940 95.548.245 350.343.565 1.121.099.408
42 42 861 11.480 111.930 850.668 5.245.786 26.978.328 118.030.185 445.891.810 1.471.442.973
43 43 903 12.341 123.410 962.598 6.096.454 32.224.114 145.008.513 563.921.995 1.917.334.783
44 44 946 13.244 135.751 1.086.008 7.059.052 38.320.568 177.232.627 708.930.508 2.481.256.778
45 45 990 14.190 148.995 1.221.759 8.145.060 45.379.620 215.553.195 886.163.135 3.190.187.286
46 46 1.035 15.180 163.185 1.370.754 9.366.819 53.524.680 260.932.815 1.101.716.330 4.076.350.421
47 47 1.081 16.215 178.365 1.533.939 10.737.573 62.891.499 314.457.495 1.362.649.145 5.178.066.751
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