Dividing the permutation count by r! yields the number of unordered groups because each specific set of r items can be arranged in r! different orders. Since combinations ignore internal order, all r! permutations of a single group correspond to just one combination.
Conditions: The selection is without repetition.; The items are distinct.; We are converting from ordered selections (permutations) to unordered selections (combinations).
Dividing the permutation count by r! yields the number of unordered groups because each specific set of r items can be arranged in r! different orders. Since combinations ignore internal order, all r! permutations of a single group correspond to just one combination.
Conditions: The selection is without repetition.; The items are distinct.; We are converting from ordered selections (permutations) to unordered selections (combinations).
We divide by r! because the permutation count includes all possible internal orderings of each selected group. Since combinations are unordered selections, these internal orderings are redundant.
Conditions: The selection is made without repetition.; Order does not matter in the final count.
We divide by r! because the permutation count includes all possible internal orderings of each selected group. Since combinations are unordered selections, these internal orderings are redundant.
Conditions: The selection is made without repetition.; Order does not matter in the final count.