Permutations

Review: (Counting Principle)1.) Carol has 4 skirts, 3 blouses and 3 pairs of shoes. How many different outfits are possible?

2.) A bike license plate consists of one letter followed by three numbers.  a.) How many license plates can be made if    numbers can repeat?

 b.) How many license plates can be made if    numbers are not allowed to repeat?

Factorial

1.) 5!  2.) 8!

3.) There are 4 people in a line outside a movie theatre. How many different ways can you arrange them?

Permutation- An arrangement in which order is important

(AB and BA are different permutations because the order is different even though the letters are the same)

Selecting a first place, second place and a third place.

Arrangement 1:1st - Mike2nd - Joe3rd - Will  

is different than

Ex:

Arrangement 2:1st - Joe2nd - Will3rd - Mike  

Even though it is the same people, they are in a different order

Permutation Notation:nPr

n = total number of items r = number choosing

1.) 6P2  2.) 8P3 

3.) 5P5  4.) 70P2 

3.) There are 5 contestants in the Mr. TEMS pageant. How many permutations (arrangements) are possible if there is a 1st, 2nd, and 3rd place?

4.) There are 50 numbers on a standard combination lock. How many 3-number arrangements are possible if no number can be repeated?

5.) There are 5 people in a group, only 2 can be lined up. How many different ways can you line them up?    

3.) How many different 7 digit phone numbers can you make?

4.) Four Olympic gold medalist will pose together for a picture. How many different ways can they stand side-by-side in the photo?

Demonstrate Understanding

1.) 10P4 2.) 7P3

6.) You have 9 books and want to display 5 on a shelf. How many different 5-book arrangements are possible?

7.) Class officers are president, vice-president, secretary and treasurer. From a class of 25 students, how many different groups of officers could students elect?

5.) You have four posters to hang in your room. You want to put one poster on each wall. how many ways can you arrange the posters?