What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate? Permutations count the number of different arrangements of r out of n items, while combinations count the number of groups of r out of n items. Both permutations and combinations count the number of different arrangements of r out of n items. Combinations count the number of different arrangements of r out of n items, while permutations count the number of groups of r out of n items. Both permutations and combinations count the number of groups of r out of n items.

Permutation is the different possible arrangements or different possible order taking by the given things, objects ,words and numbers. it is also know rearranging.

Result are vary with different conditions Like Repetition is allowed or Repetition is not allowed

In mathematics we denote permutation by [tex]{\textup{n}p_{r}}[/tex] no of permutation of n taken r at a time.

Combination is a selection of some specific item or all items at a time from a collection is known as combination. It is denote by [tex]{\textup{n}c_{r}}[/tex] number of combination of n different things taken r at a time

Eg. We have to choose 2 boys in group of 5 so, we can choose by many ways

Combination is widely used in lottery system.

So

Permutation count the number of different arrangements pf r out of n items, while combination count the number of group of r out of n items.