Lesson 13.2 Find Probabilities Using Permutations

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Presentation transcript:

Lesson 13.2 Find Probabilities Using Permutations Essential Question: How do you use the formula for permutations?

Before we start… How many ways can you order the letters A and B? Write out the orders. How many ways can you order the letters A, B and C? Write out the orders.

What is a permutation? An arrangement of objects in which order is important. The 6 possible permutations of the letters A, B and C are: ABC ACB BAC BCA CAB CBA

How do you calculate a permutation? Calculating a permutation can be done 2 ways: The number of permutations of n objects The number of permutations of n objects taken r at a time

How do you calculate the number of permutations of n objects? You use the formula: Remember n! is n factorial, which is the product of the integers from 1 to n.

How do you calculate the number of permutations of n objects taken r at a time? You use the formula: Here you are picking r of the n objects.

In how many ways can you arrange all of the letters in the word JULY?

How many ways can you arrange the letters in the word MOUSE? How many ways can you arrange 3 of the letters in the word ORANGE?

Volleyball There are 8 volleyball teams in a tournament Volleyball There are 8 volleyball teams in a tournament. In how many ways can teams place first, second, third and fourth?

A travel agency is planning a vacation package in which travelers will visit 5 cities around Europe. How many ways can the agency arrange the 5 cities along the tour?

Twelve marching bands are entered in a competition Twelve marching bands are entered in a competition. How many ways can first, second, and third place be awarded?

Ralph must choose a 4-digit code for access to an online computer game Ralph must choose a 4-digit code for access to an online computer game. Each digit in the code may be any of the digits 0 – 9 and none may be repeated. How many different codes could Ralph choose from?

For a town parade, you will ride on a float with your soccer team For a town parade, you will ride on a float with your soccer team. There are 12 floats in the parade, and their order is chosen at random. Find the probability that your float is first and the float with the school chorus is second.

A bag contains 5 cards numbered 1 – 5 A bag contains 5 cards numbered 1 – 5. You draw one card at a time until draw all 5 cards. What is the probability of drawing the card numbered 1 first and the card numbered 2 second?

There are 9 players on a softball team There are 9 players on a softball team. Each game the batting order is randomly fixed. Find the probability that you are chosen to bat first, and your best friend is chosen to bat second.

How do you use the formula for permutations?

Ticket Out the Door Six friends go to a movie theater. In how many different ways can they sit together in a row of 6 empty seats?