Apply the Counting Principle and Permutations Lesson 10.1 AlgebraII

Agenda Lesson 10.1 Homework 10.1; On pages do exercises 1, 4, 5, 9, 11, 16, 18, 23, 28, 34, 38, 43, 48, 63.

Apply the Counting Principle and Permutations

You are a member of the math team and the team has 3 different t-shirts that they wear in competition and 2 different coordinating pairs of sweatpants. The team wants to have a different uniform for every competition that they have. How many different competitions can the team attend without repeating a uniform? By the counting principle… 2x3=6 EXAMPLE SLIDE

Apply the Counting Principle and Permutations

We can also make a tree diagram for this problem: DEFINITION SLIDE

Apply the Counting Principle and Permutations You are a member of the math team and the team has 3 different t-shirts that they wear in competition and 2 different coordinating pairs of sweatpants. The team wants to have a different uniform for every competition that they have. How many different competitions can the team attend without repeating a uniform? Now let’s add 5 hats to the mix… By the counting principle… 2x3x5=30 EXAMPLE SLIDE

Apply the Counting Principle and Permutations If you look at California plates you will see that they start with a single digit, then are followed by 3 letters then followed by three numbers. The letters I,O and Q are may not be used in the 1 st or 3 rd position on the plate… How many unique standard plates can be issued before California needs to go to a new system… There are 10 digits available and there are 26 letters in the alphabet. EXAMPLE SLIDE

Apply the Counting Principle and Permutations 10x23x26x23x10x10x10… that’s a lot! 137,540,000 There are about 25 million cars registered in the state of California. SOLUTION SLIDE

Apply the Counting Principle and Permutations Now let’s talk about permutations… Remember Johanna from the Pizza parlor… she likes ice cream cones. The store that she visits has 24 flavors of ice cream. It’s important to her which flavor scoop is on top. After all, she says, eating chocolate and then vanilla is a different taste experience from eating vanilla and then chocolate. She always orders two different flavors. How many different two-scoop ice cream cones can Johanna create? EXAMPLE SLIDE

Apply the Counting Principle and Permutations

Do problems 9, 13 and 15 from Practice B

Apply the Counting Principle and Permutations

Do problems 17, 19 and 24 from Practice B.

Apply the Counting Principle and Permutations We can also look at the different permutations when we have repetitions… The letters a, a and b. If the two a’s are how many different ways can we arrange these letters to form unique words?

Apply the Counting Principle and Permutations The letters a, a and b. If the two a’s are how many different ways can we arrange these letters to form unique words? aab aba baa… so how do figure this out.. If we had three different letters it would be 3x2x1 because of the number of permutations. What process can we find to do this systematically?

Apply the Counting Principle and Permutations

Find the number of distinguishable permutations of the letters in the word: 1.MALL 2.KAYAK 3.MISSISSIPPI EXAMPLE SLIDE

Apply the Counting Principle and Permutations