PERMUTATIONS AND COMBINATIONS In many probability problems it
PERMUTATIONS AND COMBINATIONS
� In many probability problems, it is necessary to find the TOTAL number of outcomes. This can be a daunting task if there a lot of outcomes � Today we are going to talk about techniques for finding such numbers
Fundamental Counting Rule � Is for a sequence of two events, in which the 1 st event can occur in m different ways and the 2 nd can occur in n different ways, the events together can occur in total of m*n ways. � This rule extends to situations involving 2 or more events
Example 1 � There are four blood types: A, B, AB, and O. Blood can also be RH+ and RH-. Finally, a blood donor can be classified as either male or female. How many different ways can a donor have his or her blood labeled?
Example 2 � Next semester, you are planning to take three courses—Math, English, and humanities. There are 8 sections of math, 5 of English, and 4 of humanities that you find suitable. Assuming no scheduling conflicts, how many different three-course schedules are possible?
Ordering Things � Sometimes we need to know how many ways certain things can be arranged � The key thing to notice is whether or not the order of the things is important
Permutations (Picky) �A permutation is an arrangement of objects where order IS important. � Eg. Putting books on a shelf, lining up for a team picture, … � FCP is a type of a permutation.
Formula � That means “n permutate r” � n is the total and r is how many you are using
Example 3 � Consider the students AJ, Kevin, David, and Bill sitting in a row. How many ways can we rearrange those boys?
ORDER: � Remember that we said order was important here. � If I switch Kevin and David, then the arrangement is NOT the same anymore � Thus the order matters…
Calculator Steps: 1. 2. 3. 4. 5. 6. Type your n (total number of objects) Go to math Tab over to PRB #2 Type your r (how many you are using) Enter
Example 4 � Given seven boys on a sports team, how many ways can they line up in a row of 4 side by side to take a picture?
Example 5 � How many different area codes are possible if it cannot begin with 0?
Combinations (Chill) �A combination is arranging things where order IS NOT important � Eg. putting toppings on a pizza, selecting people to put in groups, …
Formula: �n is still the total number and r is still how many you are choosing � Read as “n choose r” � Also in calculator, same steps except you choose #3 instead of #2
Example 6 �A certain pizza parlor offers 20 different topping choices and is running a special on a large 3 topping pizza. How many pizza choices are possible?
Example 7 � There are 20 cats and 14 dogs at a pound. I wish to adopt two of each animal. How many possibilities are available for me to save?
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