12 1 The Fundamental Counting Principal & Permutations

12.1 The Fundamental Counting Principal & Permutations P. 701

The Fundamental Counting Principal ,[object Object],[object Object],[object Object],[object Object],[object Object]

3 or more events: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

Fund. Counting Principal with repetition ,[object Object],[object Object],[object Object],[object Object],[object Object]

How many plates are possible if digits and numbers cannot be repeated? ,[object Object],[object Object],[object Object],[object Object]

Phone numbers ,[object Object],[object Object],[object Object]

Testing ,[object Object],[object Object],[object Object]

Using Permutations ,[object Object]

There are 6 permutations of the letters A, B, &C ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],You can use the Fund. Counting Principal to determine the number of permutations of n objects. Like this ABC. There are 3 choices for 1 st # 2 choices for 2 nd # 1 choice for 3 rd . 3*2*1 = 6 ways to arrange the letters

In general, the # of permutations of n objects is: ,[object Object]

12 skiers… ,[object Object],[object Object],[object Object]

Factorial with a calculator: ,[object Object],[object Object]

Back to the finals in the Olympic skiing competition. ,[object Object],[object Object],[object Object],[object Object]

Permutation of n objects taken r at a time ,[object Object]

Back to the last problem with the skiers ,[object Object],[object Object],[object Object],[object Object]

10 colleges, you want to visit all or some. ,[object Object],[object Object],[object Object],[object Object],[object Object]

How many ways can you visit all 10 of them: ,[object Object],[object Object],[object Object],[object Object],[object Object]

So far in our problems, we have used distinct objects. ,[object Object],[object Object],[object Object],[object Object],[object Object]

Permutations with Repetition ,[object Object],[object Object]

Find the number of distinguishable permutations of the letters: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Find the number of distinguishable permutations of the letters: ,[object Object],[object Object],[object Object],[object Object]

A dog has 8 puppies, 3 male and 5 female. How many birth orders are possible ,[object Object],[object Object]

12 1 The Fundamental Counting Principal & Permutations

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12 1 The Fundamental Counting Principal & Permutations