Suppose we have a set containing n elements, and we want to calculate the number of combinations of all elements in this set. According to the formula in combinatorial mathematics, the answer to this question is 2 (n * (n-1))/(n * (n-1)).
Let's explain this formula in detail. First of all, we know that the elements in a set can be arranged in different orders, so we need to calculate all possible arrangements. For a set containing n elements, there is always n! There are three arrangements, namely n * (n-1) * (n-2) * ... * 3 * 2 *1.
However, we need to note that for each element, we have two choices: choose it or not. Therefore, we need to divide the total arrangement by the n power of 2, because each element has two choices.
Therefore, the final combination number is 2 (n * (n-1))/(n * (n-1)).
For example, suppose we have a set {A, b, C} with three elements. We can use the above formula to calculate all possible combinations:
2^((3*(3- 1))/(3*(3- 1)))=2^((6)/6)=4
Therefore, there are four possible combinations in sets {a}, {b}, {c}, {a, b, c}.
To sum up, Formula 2 (n * (n-1)) in combinatorial mathematics can be used to calculate all possible combinations of a set. Based on the concept of permutation and combination, the formula determines the number of combinations by considering whether each element is selected.