Permutations

Lesson 10 – 4

Vocabulary• Permutation – an arrangement or listing of

objects in which order is important.• Example: the first three classes of the day are

math, science, and history. How many ways can you arrange your classes?– To solve, think about how many choices are

possible for 1st Period?– Then, how many choices are left for 2nd Period?– How many choices left for 3rd period?– Now, multiply, 3 x 2 x 1 = 6 arrangements.

Proof!

M – math

S – science

H – history

1st, 2nd, 3rd

MSH SMH HMS

MHS SHM HSM

Things to Know

# 1: How to recognize when it’s a permutation and not combination?

Look for key words like; arranged, order, how many ways, permutation, etc…

How many permutations are there from using the letters in the word LETTERS?

7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

Things to Know# 2: Is there a symbol for permutation?

n! ‘the exclamation mark’

The ! means factorial. Factorial means to multiply by the next smallest whole number until you reach x 1.

Example: 5!means to multiply 5 x 4 x 3 x 2 x 1 =

10!means: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =

Things to Know# 3: Can I stop before reaching 1? If the question is asking for only a certain

amount, then ‘yes’.Example: How many 3 digit outcomes be

formed from even digits, if no numbers can be used more than once?First, your digits to choose from: 2, 4, 6, 8So, 1st digit: 4 choices; 2nd digit: 3 choices

3rd digit: 2 choicesMultiply 4 x 3 x 2 = 24 outcomes.

Practice• How many 3 digit area codes can be

created if no digit repeats itself?720 area codes

• 5 passengers are sitting in a car. How many different seating arrangements can there be?120 seating arrangements

• There are 90 ways for two students to become president and vice president of student council. How many people were in the election?10 students

Practice• You have five seasons of your favorite TV

show on DVD. If you randomly select two of them from a shelf, what is the probability that you will select season one first and season two second?1 / 20

• A password consists of four letters, of which none are repeated. What is the probability that a person could guess the entire password by randomly selecting the four letters?1 / 358,800