Probability

=Chapter 15 Review=

Permutations
What is the factorial?//**
 * //What key information do you need to know to be able to solve permutations? What are some helpful tips?

Order matters when solving a permutation.

Permutation is more about arrangements. In addition permutations do not repeat the number. When a problem ask for instance how many people can u align it would be a permutation.

You need to know what the order of the objects must be, and how many object there are. The number of the objects P the number of slots in the order. the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) =4 · 3 · 2 · 1= 24. Symbol: n!, where n is the given integer.

__If the question is regarding a circle you always subract one from the total amount of people when doing factorial.__ You need to know if there are repeats allowed or none. Also you need to know if certain numbers cannot be in certain spots. Like no 0's first.

Combinations
//**What are some words used with combinations to distinguish them from permutations? How else can you tell the difference? What tips do you have for someone who is getting confused?**//

When the problem indicates commitees, or a large set of items and not caring what order a group is selected, use a combination. For example there are 5 people in a group and they need to pick 3 to lead. The problem would be a combination because the order does not matter. However, if a the problem ask how many people can be arranged with specific roles mentioned, it would be a permutation.

Combinations don't point out the order needed for the objects too well, permutations are very clear on that point I don't have any tips, except to read the question as many times as needed so you don't look over a word.

Example: You have five places left for stamps in your stamp book and you have eight stamps. How many different ways can you select five? Answer: 8!/(5!3!) =8•7•6/(3•2)= 56. Think of putting them in slots, the first has eight choices, the next slot has seven choices and so forth as demonstrated. 8 x 7 x 6 x 5 x 4

For combinations you do not need to know the order. So anything can be first.



Probability
//**What are the rules for probability? When do you need to subtract out a common item? What are some overall tips?**//

Probability is the amount you have over the total amount. For OR problems, when there is a common item such as Aces and black cards you must subtract out any black aces. I.E. Find the probability of selecting an ACE or BLACK card =4/52 + 26/52 - 2/52 (black aces)= 28/52 and reduce it. =7/13

Problems by You - permutations/combinations/counting principle/probability
1) How many different ways can 5 people line up? (120 from 5! or 5P5)
 * //Add your problem (as the next one with a number)for review and the answer in parentheses and how to get it.//**

2) If there are 10 people sitting at a round table how many differnt orders can i put them in? 9!

3. If there are 6 cars how many ways can i line them up. 6! (6 x 5 x 4 x 3 x 2 x1)= 720

4) If I was sitting in a row of 6 people and I had to be the last one, how many ways can people be arranged?