Combinations calculation for the Euro Millions

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

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NUMBER2 Num3 Num4 Num5 Num6 Num7 Num8 Num9 Num10 Num
5101051
615201561
72135352171
8285670562881
93684126126843691
104512021025221012045101
11551653304624623301655511
126622049579292479249522066
13782867151.2871.7161.7161.287715286
14913641.0012.0023.0033.4323.0032.0021.001
151054551.3653.0035.0056.4356.4355.0053.003
161205601.8204.3688.00811.44012.87011.4408.008
171366802.3806.18812.37619.44824.31024.31019.448
181538163.0608.56818.56431.82443.75848.62043.758
191719693.87611.62827.13250.38875.58292.37892.378
201901.1404.84515.50438.76077.520125.970167.960184.756
212101.3305.98520.34954.264116.280203.490293.930352.716
222311.5407.31526.33474.613170.544319.770497.420646.646
232531.7718.85533.649100.947245.157490.314817.1901.144.066
242762.02410.62642.504134.596346.104735.4711.307.5041.961.256
253002.30012.65053.130177.100480.7001.081.5752.042.9753.268.760
263252.60014.95065.780230.230657.8001.562.2753.124.5505.311.735
273512.92517.55080.730296.010888.0302.220.0754.686.8258.436.285
283783.27620.47598.280376.7401.184.0403.108.1056.906.90013.123.110
294063.65423.751118.755475.0201.560.7804.292.14510.015.00520.030.010
304354.06027.405142.506593.7752.035.8005.852.92514.307.15030.045.015
314654.49531.465169.911736.2812.629.5757.888.72520.160.07544.352.165
324964.96035.960201.376906.1923.365.85610.518.30028.048.80064.512.240
335285.45640.920237.3361.107.5684.272.04813.884.15638.567.10092.561.040
345615.98446.376278.2561.344.9045.379.61618.156.20452.451.256131.128.140
355956.54552.360324.6321.623.1606.724.52023.535.82070.607.460183.579.396
366307.14058.905376.9921.947.7928.347.68030.260.34094.143.280254.186.856
376667.77066.045435.8972.324.78410.295.47238.608.020124.403.620348.330.136
387038.43673.815501.9422.760.68112.620.25648.903.492163.011.640472.733.756
397419.13982.251575.7573.262.62315.380.93761.523.748211.915.132635.745.396
407809.88091.390658.0083.838.38018.643.56076.904.685273.438.880847.660.528
4182010.660101.270749.3984.496.38822.481.94095.548.245350.343.5651.121.099.408
4286111.480111.930850.6685.245.78626.978.328118.030.185445.891.8101.471.442.973
4390312.341123.410962.5986.096.45432.224.114145.008.513563.921.9951.917.334.783
4494613.244135.7511.086.0087.059.05238.320.568177.232.627708.930.5082.481.256.778
4599014.190148.9951.221.7598.145.06045.379.620215.553.195886.163.1353.190.187.286
461.03515.180163.1851.370.7549.366.81953.524.680260.932.8151.101.716.3304.076.350.421
471.08116.215178.3651.533.93910.737.57362.891.499314.457.4951.362.649.1455.178.066.751
481.12817.296194.5801.712.30412.271.51273.629.072377.348.9941.677.106.6406.540.715.896
491.17618.424211.8761.906.88413.983.81685.900.584450.978.0662.054.455.6348.217.822.536
501.22519.600230.3002.118.76015.890.70099.884.400536.878.6502.505.433.70010.272.278.170