The number of k-combinations for all k is the number of subsets of a set of n elements. We compute the total combinations by using the Combination formula. So the rule is to pick five numbers from 1 to 50.
There are several ways to see that this number is 2 nIn terms of combinations which is the sum of the nth row counting from 0 of the binomial coefficients in Pascals triangleThese combinations subsets are enumerated by the 1 digits of the set of base 2 numbers counting from 0 to 2 n.
N C r 10. N n - r. In fact there is a formula from Combinations for working out the value at any place in Pascals triangle. Formula for Combinations of n Distinct Objects Given latexnlatex distinct objects the number of ways to select latexrlatex objects from the set is latextextCleftnrrightfracnrleftn-rrightlatex.