Permutations and Combinations

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# Permutations and Combinations - PowerPoint PPT Presentation

Permutations and Combinations. Permutations and Combinations. Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

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Presentation Transcript

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Permutation – it is a set of “n” distinct items taken “r” at a time. It is an arrangement of the “r” objects in a specific order without repetition. So order matters… AB is not the same as BA

Think of a permutation as “all possible ways of doing something”

Permutations and Combinations

Example # 2 : An airline company has to fill 2 pilot positions and it has 15 candidates to choose from. How many different ways can the positions be filled ?

Permutations and Combinations

Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ?

Permutations and Combinations

Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ?

Let’s try the shortcut …

n = 18

r = 5

So I am going to start to count down from 18 and take the first 5 numbers…

Permutations and Combinations

Example # 3 : Mr. Hartman has 18 computers in his classroom. If 5 students show up for make – up work, how many different ways could the students be seated at the computers ?

Let’s try the shortcut …

n = 18

r = 5

So I am going to start to count down from 18 and take the first 5 numbers…

Permutations and Combinations

Combination – kind of like a permutation but the order doesn’t matter.

Example : How many combinations of flavors can I choose if I am getting 3 scoops of ice cream and there are 10 flavors available ?

Let’s say I choose chocolate, vanilla, and strawberry. The order doesn’t matter, I could order vanilla, strawberry, and chocolate.

Permutations and Combinations

Let’s try the shortcut in this example :

There are 15 freshman trying out for the swim team. The coach can only choose 6 of them. How many different 6 member squads can the coach select ?

Permutations and Combinations

Let’s try the shortcut in this example :

There are 15 freshman trying out for the swim team. The coach can only choose 6 of them. How many different 6 member squads can the coach select ?

n = 15

r = 6

Count down from 15 for 6 numbers and divide by r!