To determine the number of combinations possible with 25 numbers, we need to clarify if we are referring to combinations of a specific size or all possible combinations.
If we consider combinations of all possible sizes (from size 0 to size 25), we can use the concept of the power set. The power set is the set of all subsets of a given set. For a set with n elements, the number of subsets (combinations) is given by 2n.
In this case, with n being 25:
225 = 33,554,432
This means that when considering all possible combinations of any size (including the empty set), there are 33,554,432 different combinations of 25 numbers.
However, if you are looking for combinations of a specific size, the formula for combinations (denoted as C(n, r) or nCr) is:
C(n, r) = n! / (r! * (n – r)!)
Where n is the total number of items (25 in this case) and r is the number of items to choose. You would need to specify the value of r to get the number of combinations of that specific size.