Final answer:
The key difference between permutation and combination formulas is that permutations consider the order of arrangement important, while combinations do not. Permutations are calculated with nPr = n! / (n - r)!, while combinations use nCr = n! / (r! * (n - r)!).
Step-by-step explanation:
The difference between the permutation formula and the combination formula lies in the consideration of order. A permutation is an arrangement of objects where the order is important, and it is calculated using the formula nPr = n! / (n - r)!, where n is the total number of objects, and r is the number of objects to be arranged. On the other hand, a combination is a selection of objects where the order does not matter, calculated by the formula nCr = n! / (r! * (n - r)!).
For example, the number of permutations of 4 different objects is 4! (4 factorial, which is 4·3·2·1), yielding 24 different arrangements. This exhaustive enumeration of permutations is useful to understand why 4·3·2·1 is an appropriate way to count permutations. When it comes to combinations, since the order does not matter, the number will be less than the permutations for the same values of n and r.