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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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Permutations and Combinations

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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

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

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

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

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

Permutations and Combinations

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!

Permutations and Combinations