Permutation means when the order is important.

Formula: nPr=n!/(n-r)!

Combination means when the order is not important.

Formula: nCr=n!/(n-r)!r!

Example 1.

In how many ways can a beach with ten members choose 5
different life guards?

10P5

10!/5!=

10x9x8x7x6x5x4x3x2x1=362880/5x4x3x2x1=120
So the final answer is 30240.

Example 2.
A football team has a total of fifty players on the team and the coach needs to make five of them team leaders or captains. How many team leaders can be made if the order of the picking is not considered important?

50C5

50!/45!5!=30510144000

Example 3.

If a teacher had a class of twenty studens and gave five students books, how many ways can the books are given if they are all different?

20P5

20!/15!= 1860480