Probability with Probability with Permutations and Permutations and

CombinationsCombinations

Advanced Math TopicsAdvanced Math Topics

Probability with Combinations and Probability with Combinations and PermutationsPermutations

Follow these steps:Follow these steps: 1. Determine how many 1. Determine how many

selections/arrangements meet the conditions selections/arrangements meet the conditions of the problemof the problem

2. Use the FCP to find the number of 2. Use the FCP to find the number of successessuccesses

3. Find the number of s + f (total 3. Find the number of s + f (total selections/arrangements)selections/arrangements)

4. Write a fraction to find the probability4. Write a fraction to find the probability

Probability with CombinationsProbability with Combinations

Monica has a collection of 32 CD’s- 18 R&B and Monica has a collection of 32 CD’s- 18 R&B and 14 rap. As she is leaving for a trip, she 14 rap. As she is leaving for a trip, she randomly chooses 6 CD’s to take with her. What randomly chooses 6 CD’s to take with her. What is the probability that she selects 3 R&B and 3 is the probability that she selects 3 R&B and 3 rap?rap? Step 1: Determine how many 6 CD combinations Step 1: Determine how many 6 CD combinations

meet the conditionsmeet the conditions Step 2: Multiply to find the number of successesStep 2: Multiply to find the number of successes Step 3: Find s + fStep 3: Find s + f Step 4: Determine the probability by dividing s by s + fStep 4: Determine the probability by dividing s by s + f

A board ggame is played with tiles and letters on A board ggame is played with tiles and letters on one side. There are 56 tiles with consonants and one side. There are 56 tiles with consonants and 42 tiles with vowels. Each player must choose 42 tiles with vowels. Each player must choose seven of the tiles at the beginning of the game. seven of the tiles at the beginning of the game. What is the probability that a player selects four What is the probability that a player selects four consonants and three vowels?consonants and three vowels? Step 1: How many selections meet the conditionsStep 1: How many selections meet the conditions Step 2: Find number of successesStep 2: Find number of successes Step 3: Find s + fStep 3: Find s + f Step 4: Determine ProbabilityStep 4: Determine Probability

Probability with PermutationsProbability with Permutations

Ramon has five books on the floor, one for each of his Ramon has five books on the floor, one for each of his classes: Algebra 2, Chemistry, English, Spanish, and classes: Algebra 2, Chemistry, English, Spanish, and History. Ramon is going to put the books on a shelf. If he History. Ramon is going to put the books on a shelf. If he picks the books up at random and places them ina row picks the books up at random and places them ina row on the same shelf, what is the probability that his on the same shelf, what is the probability that his English, Spanish, and Algebra 2 books will be the English, Spanish, and Algebra 2 books will be the leftmost books on the shelf, but not necssarily in that leftmost books on the shelf, but not necssarily in that order?order?

Step 1: Determine how many arrangements meet the conditionsStep 1: Determine how many arrangements meet the conditions Step 2: Find the number of successesStep 2: Find the number of successes Step 3: Find s + fStep 3: Find s + f Step 4: Determine the probabilityStep 4: Determine the probability

For next semester, Alisa has signed up for English, For next semester, Alisa has signed up for English, Precalculus, Spanish, Geography, and chemistry Precalculus, Spanish, Geography, and chemistry classes. If class schedules are assigned randomly and classes. If class schedules are assigned randomly and each class is equally likely to be at any time of day what each class is equally likely to be at any time of day what is the probability that Alisa’s first two classes in the is the probability that Alisa’s first two classes in the morning will be Precalculus and Chemistry, in either morning will be Precalculus and Chemistry, in either order?order?

Step 1: Find how many arrangements meet the conditionsStep 1: Find how many arrangements meet the conditions Step 2: Find the number of successesStep 2: Find the number of successes Step 3: Find s + fStep 3: Find s + f Step 4: Find the probablityStep 4: Find the probablity