Combinations calculation for the NY Lotto

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

NUMBER3 Num4 Num5 Num6 Num7 Num8 Num9 Num10 Num
6201561
735352171
85670562881
984126126843691
1012021025221012045101
111653304624623301655511
1222049579292479249522066
132867151.2871.7161.7161.287715286
143641.0012.0023.0033.4323.0032.0021.001
154551.3653.0035.0056.4356.4355.0053.003
165601.8204.3688.00811.44012.87011.4408.008
176802.3806.18812.37619.44824.31024.31019.448
188163.0608.56818.56431.82443.75848.62043.758
199693.87611.62827.13250.38875.58292.37892.378
201.1404.84515.50438.76077.520125.970167.960184.756
211.3305.98520.34954.264116.280203.490293.930352.716
221.5407.31526.33474.613170.544319.770497.420646.646
231.7718.85533.649100.947245.157490.314817.1901.144.066
242.02410.62642.504134.596346.104735.4711.307.5041.961.256
252.30012.65053.130177.100480.7001.081.5752.042.9753.268.760
262.60014.95065.780230.230657.8001.562.2753.124.5505.311.735
272.92517.55080.730296.010888.0302.220.0754.686.8258.436.285
283.27620.47598.280376.7401.184.0403.108.1056.906.90013.123.110
293.65423.751118.755475.0201.560.7804.292.14510.015.00520.030.010
304.06027.405142.506593.7752.035.8005.852.92514.307.15030.045.015
314.49531.465169.911736.2812.629.5757.888.72520.160.07544.352.165
324.96035.960201.376906.1923.365.85610.518.30028.048.80064.512.240
335.45640.920237.3361.107.5684.272.04813.884.15638.567.10092.561.040
345.98446.376278.2561.344.9045.379.61618.156.20452.451.256131.128.140
356.54552.360324.6321.623.1606.724.52023.535.82070.607.460183.579.396
367.14058.905376.9921.947.7928.347.68030.260.34094.143.280254.186.856
377.77066.045435.8972.324.78410.295.47238.608.020124.403.620348.330.136
388.43673.815501.9422.760.68112.620.25648.903.492163.011.640472.733.756
399.13982.251575.7573.262.62315.380.93761.523.748211.915.132635.745.396
409.88091.390658.0083.838.38018.643.56076.904.685273.438.880847.660.528
4110.660101.270749.3984.496.38822.481.94095.548.245350.343.5651.121.099.408
4211.480111.930850.6685.245.78626.978.328118.030.185445.891.8101.471.442.973
4312.341123.410962.5986.096.45432.224.114145.008.513563.921.9951.917.334.783
4413.244135.7511.086.0087.059.05238.320.568177.232.627708.930.5082.481.256.778
4514.190148.9951.221.7598.145.06045.379.620215.553.195886.163.1353.190.187.286
4615.180163.1851.370.7549.366.81953.524.680260.932.8151.101.716.3304.076.350.421
4716.215178.3651.533.93910.737.57362.891.499314.457.4951.362.649.1455.178.066.751
4817.296194.5801.712.30412.271.51273.629.072377.348.9941.677.106.6406.540.715.896
4918.424211.8761.906.88413.983.81685.900.584450.978.0662.054.455.6348.217.822.536
5019.600230.3002.118.76015.890.70099.884.400536.878.6502.505.433.70010.272.278.170
5120.825249.9002.349.06018.009.460115.775.100636.763.0503.042.312.35012.777.711.870
5222.100270.7252.598.96020.358.520133.784.560752.538.1503.679.075.40015.820.024.220
5323.426292.8252.869.68522.957.480154.143.080886.322.7104.431.613.55019.499.099.620
5424.804316.2513.162.51025.827.165177.100.5601.040.465.7905.317.936.26023.930.713.170
5526.235341.0553.478.76128.989.675202.927.7251.217.566.3506.358.402.05029.248.649.430
5627.720367.2903.819.81632.468.436231.917.4001.420.494.0757.575.968.40035.607.051.480
5729.260395.0104.187.10636.288.252264.385.8361.652.411.4758.996.462.47543.183.019.880
5830.856424.2704.582.11640.475.358300.674.0881.916.797.31110.648.873.95052.179.482.355
5932.509455.1265.006.38645.057.474341.149.4462.217.471.39912.565.671.26162.828.356.305