Combinations calculation for the Powerball

The combination calculation for the Powerball 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 Powerball lottery?
This table provides the answers.

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NUMBER1 Num2 Num3 Num4 Num5 Num6 Num7 Num8 Num9 Num10 Num
55101051
6615201561
772135352171
88285670562881
993684126126843691
10104512021025221012045101
1111551653304624623301655511
12126622049579292479249522066
1313782867151.2871.7161.7161.287715286
1414913641.0012.0023.0033.4323.0032.0021.001
15151054551.3653.0035.0056.4356.4355.0053.003
16161205601.8204.3688.00811.44012.87011.4408.008
17171366802.3806.18812.37619.44824.31024.31019.448
18181538163.0608.56818.56431.82443.75848.62043.758
19191719693.87611.62827.13250.38875.58292.37892.378
20201901.1404.84515.50438.76077.520125.970167.960184.756
21212101.3305.98520.34954.264116.280203.490293.930352.716
22222311.5407.31526.33474.613170.544319.770497.420646.646
23232531.7718.85533.649100.947245.157490.314817.1901.144.066
24242762.02410.62642.504134.596346.104735.4711.307.5041.961.256
25253002.30012.65053.130177.100480.7001.081.5752.042.9753.268.760
26263252.60014.95065.780230.230657.8001.562.2753.124.5505.311.735
27273512.92517.55080.730296.010888.0302.220.0754.686.8258.436.285
28283783.27620.47598.280376.7401.184.0403.108.1056.906.90013.123.110
29294063.65423.751118.755475.0201.560.7804.292.14510.015.00520.030.010
30304354.06027.405142.506593.7752.035.8005.852.92514.307.15030.045.015
31314654.49531.465169.911736.2812.629.5757.888.72520.160.07544.352.165
32324964.96035.960201.376906.1923.365.85610.518.30028.048.80064.512.240
33335285.45640.920237.3361.107.5684.272.04813.884.15638.567.10092.561.040
34345615.98446.376278.2561.344.9045.379.61618.156.20452.451.256131.128.140
35355956.54552.360324.6321.623.1606.724.52023.535.82070.607.460183.579.396
36366307.14058.905376.9921.947.7928.347.68030.260.34094.143.280254.186.856
37376667.77066.045435.8972.324.78410.295.47238.608.020124.403.620348.330.136
38387038.43673.815501.9422.760.68112.620.25648.903.492163.011.640472.733.756
39397419.13982.251575.7573.262.62315.380.93761.523.748211.915.132635.745.396
40407809.88091.390658.0083.838.38018.643.56076.904.685273.438.880847.660.528
414182010.660101.270749.3984.496.38822.481.94095.548.245350.343.5651.121.099.408
424286111.480111.930850.6685.245.78626.978.328118.030.185445.891.8101.471.442.973
434390312.341123.410962.5986.096.45432.224.114145.008.513563.921.9951.917.334.783
444494613.244135.7511.086.0087.059.05238.320.568177.232.627708.930.5082.481.256.778
454599014.190148.9951.221.7598.145.06045.379.620215.553.195886.163.1353.190.187.286
46461.03515.180163.1851.370.7549.366.81953.524.680260.932.8151.101.716.3304.076.350.421
47471.08116.215178.3651.533.93910.737.57362.891.499314.457.4951.362.649.1455.178.066.751
48481.12817.296194.5801.712.30412.271.51273.629.072377.348.9941.677.106.6406.540.715.896
49491.17618.424211.8761.906.88413.983.81685.900.584450.978.0662.054.455.6348.217.822.536
50501.22519.600230.3002.118.76015.890.70099.884.400536.878.6502.505.433.70010.272.278.170
51511.27520.825249.9002.349.06018.009.460115.775.100636.763.0503.042.312.35012.777.711.870
52521.32622.100270.7252.598.96020.358.520133.784.560752.538.1503.679.075.40015.820.024.220
53531.37823.426292.8252.869.68522.957.480154.143.080886.322.7104.431.613.55019.499.099.620
54541.43124.804316.2513.162.51025.827.165177.100.5601.040.465.7905.317.936.26023.930.713.170
55551.48526.235341.0553.478.76128.989.675202.927.7251.217.566.3506.358.402.05029.248.649.430
56561.54027.720367.2903.819.81632.468.436231.917.4001.420.494.0757.575.968.40035.607.051.480
57571.59629.260395.0104.187.10636.288.252264.385.8361.652.411.4758.996.462.47543.183.019.880
58581.65330.856424.2704.582.11640.475.358300.674.0881.916.797.31110.648.873.95052.179.482.355
59591.71132.509455.1265.006.38645.057.474341.149.4462.217.471.39912.565.671.26162.828.356.305
60601.77034.220487.6355.461.51250.063.860386.206.9202.558.620.84514.783.142.66075.394.027.566
61611.83035.990521.8555.949.14755.525.372436.270.7802.944.827.76517.341.763.50590.177.170.226
62621.89137.820557.8456.471.00261.474.519491.796.1523.381.098.54520.286.591.270107.518.933.731
63631.95339.711595.6657.028.84767.945.521553.270.6713.872.894.69723.667.689.815127.805.525.001
64642.01641.664635.3767.624.51274.974.368621.216.1924.426.165.36827.540.584.512151.473.214.816
65652.08043.680677.0408.259.88882.598.880696.190.5605.047.381.56031.966.749.880179.013.799.328
66662.14545.760720.7208.936.92890.858.768778.789.4405.743.572.12037.014.131.440210.980.549.208
67672.21147.905766.4809.657.64899.795.696869.648.2086.522.361.56042.757.703.560247.994.680.648
68682.27850.116814.38510.424.128109.453.344969.443.9047.392.009.76849.280.065.120290.752.384.208
69692.34652.394864.50111.238.513119.877.4721.078.897.2488.361.453.67256.672.074.888340.032.449.328