Permutations and Combinations

We use combination and permutation to find out how any possible outcomes there are in a situation. 

You use combination when the order is unimportant. 

You use permutation when the order is important. 

Permutation formula: nPr= n!/(n-r)!

Combination formula: nCr= n!/(n-r)!r!

-Permutation Examples

Example 1: Find 7!

Answer: 5040

Example 2: In how many ways can 8 CD's be arranged on a shelf?

Answer: 40320

Example 3: If a softball league has 10 teams, how many different end of the season rankings are possible if there are no ties?

Answer: 3,628,800

Example 4:  In how many ways can a sorority of 20 members select a president, vice president, and treasury, assuming that the same person cannot hold more than one office?

Answer: 6840

Example 5:  How many different arrangements can be made using two of the letters of the word TEXAS if no letter is to be used more than once?

Answer: 20

-Combination Examples

Example 1: In a conference of 9 schools, how many intraconference football games are played during the season if the teams all play each other exactly once?

Answer: 36

Example 2: You are going to draw 4 cards from a standard deck of 52 cards.  How many different 4 card hands are possible? 

Answer: 270,725