Permutation and Combination

Permutation and Combination

Factorial Notation

Both permutation and combination expressions uses the symbol "!" which is called factorial. It indicates that if you have n!, you are trying to get the product of all the integers less than or equal to n.

The next slide will give you a discussion of how to simplify factorial notation.

Exercises

Factorial Notation

Multiple Choice

Which of the following is the expanded form of 5!

• 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1

• 4 ∙ 3 ∙ 2 ∙ 1

• 5 ∙ 1

• 5 + 4 + 3 + 2 + 1

Multiple Choice

What is the value of 7!

• 4,050

• 5,040

• 27

• 49

Multiple Choice

Evaluate the factorial notation

 $\frac{5!}{3!}$  

• 4

• 5

• 9

• 20

Multiple Choice

What is the value of

 $\frac{10!}{2!5!}$  

• 30,240

• 15,120

• 1

• 0

Permutation

Since you have learned how to use factorial notation, let us now have the discussion for permutation.

The next slide will give you a discussion on linear permutation.

Exercise

Linear Permutation

Multiple Choice

Solve

 $\ _4P_4$  

• 24

• 16

• 8

• 4

Multiple Choice

Solve

 $\ _8P_4$  

• 4

• 32

• 1680

• 6180

Permutation

The next video discussion will give talk about permutation with repeated elements and circular permutation.

Exercise

Circular Permutation and Permutation with Repetition

Multiple Choice

Which expression should be used to determine the number of ways you can arrange a bracelet with 12 different beads?

• $\left(12-1\right)!$

• $\frac{\left(12-1\right)!}{2}$

• $\frac{12!}{2}$

• $\frac{2!}{\left(12-1\right)!}$

Multiple Choice

Which expression will solve the number of ways you can arrange the letters of the word PRACTICE

• $\frac{10!}{2!2!}$

• $\frac{8!}{2!2!}$

• $\frac{10!}{2!}$

• $\frac{8!}{2!}$

Combination

Since we are done discussing permutation, let us now discuss combination.

We will differentiate permutation and combination.

We will also solve problems involving combination.

Activity

Submit the activity on February 24, 2021