Which formula is used to calculate a combination?

The formula for calculating a combination is expressed as nCr = n!/r!(n-r)!. This formula is used when you want to determine how many ways you can choose r items from a total of n items without regard to the order in which they are selected.

In this formula, "n!" represents the factorial of n, which is the product of all positive integers up to n. The term "r!" accounts for the arrangements of the r items selected, and "(n-r)!" accounts for the arrangements of the remaining items. By dividing n! by the product of r! and (n-r)!, the formula effectively counts only unique selections of r items from n, eliminating any considerations of order that would arise in permutations.

This is why the formula in the first choice is correct, as it accurately represents the mathematical principles behind combinations. The other formulas either misrepresent the factorial operations or pertain to permutations, which involve order and are calculated differently.