Combinations calculation for the Euro Jackpot

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

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