Combinations calculation for the New York Take 5

The combination calculation for the New York Take 5 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 New York Take 5 lottery?
This table provides the answers.

NUMBER3 Num4 Num5 Num6 Num7 Num8 Num9 Num10 Num
51051
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