12.1 & 12.2: The Fundamental Counting Principal, Permutations, & Combinations.
Counting permutations combinations
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Transcript of Counting permutations combinations
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Warm-up
What is the probability that you will pick one card that is a number 12 out of a regular deck of playing cards?
What is the probability that you will pick an even number out of the numbers 2, 4, 6, 8, 10?
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Counting PrinciplePermutationsCombinations
After today, you will be able to count outcomes, use
permutations, and use combinations.
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Bagel Mania!
Bagel Mania offers chicken, tuna, and vegetable sandwiches on plain or onion bagels. How many possible sandwiches are there?
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Tree Diagram
Chicken Tuna Vegetable
Plain Onion PlainPlain OnionOnion
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Counting Principle
To find the total number of outcomes, multiply your options together.
EX) 8 different pizza toppings and 3 types of crust (stuffed, thick, thin). How many different combinations for a one-topping pizza?
EX) Four coins are tossed.
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How many different ways can you order an ice cream if the choices are:
What is the probability the ice cream will be in a sugar cone?
Type of cone Number of scoops
Ice cream flavor
Toppings
Sugar or waffle One or two Chocolate, vanilla, coffee or pistachio
Sprinkles, syrup, or none
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Permutations
Permutation- an arrangement or listing in which order is important.
How many arrangements are possible with a 4-swimmer relay? 4 x 3 x 2 x 1 or 4P4 in your calculator
How many arrangements are possible with 5 swimmers for a 4-swimmer relay? 5 x 4 x 3 x 2 or 5P4 in your calculator
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Permutations
Find P(8,3) P(8,3) means the number of orders of 8 things
taken 3 at a time.
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Combinations
Combination- arrangements where order is NOT important.
Examples:
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Combinations
Ex) In gym class Mr. Merrill picked 10 students to compete in the 100m dash. The top three finishers each received a free t-shirt. How many combinations of winners could there be?
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Permutation OR Combination?
Four books in a row 6 CDs from a group of 20 A team of 6 players from 12 Ten people in line to buy tickets
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Permutations
What is 4! 4! Is read as “four factorial”
Find 6!