December 16 2014 WarmUp A computer program requires

December 16, 2014 Warm-Up A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Question: If the first 3 digits must be even how many outcomes are possible?

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers?

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? Sample Space of the even numbers are 2, 4 and 6 meaning you have 3 outcomes or options. 3 There are three even numbers to choose from. So, there are three ways that the first digit could be even.

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? 3 2 Now there are only two even numbers to choose from. So, there are two ways that the second digit could be even.

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? 3 2 1

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? 3 2 1 4 Now we come to the fourth digit, and there are four odd numbers to choose from. So, there are four ways that the fourth digit could be odd.

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? 3 2 1 4 3 2 1 Using this same logic, we can determine the different possibilities for the remaining digits.

Permutations A computer program requires the user to enter a 7 -digit registration code made up of the digits 1, 2, 4, 5, 6, 7, and 9. Each number has to be used, and no number can be used more than once. Q 1) How many total outcomes would you have if the first three digits of the code are even numbers? 3 2 1 4 3 2 1 So, the number of favorable outcomes is 3 * 2 * 1 * 4 * 3 * 2 * 1 or 144.

Review of Permutation • It is the arrangement of a set of objects in a particular order. • Order matters Example: Suppose you have to write 5 thank you notes to 5 people. How many ways can you choose the order in which to write the notes?

Remember think through step by step… • At the beginning you have 5 thank you notes to choose from • After writing one note you have 4 left to choose from • After writing two notes you have 3 left to choose from • This pattern continues until you are out of thank you notes to write. 5 x 4 x 3 x 2 x 1 = ? ? ? ways

Combinations An arrangement or listing in which order is not important is called a combination. For example, if you are choosing 2 salad ingredients from a list of 10, the order in which you choose the ingredients does not matter. Combination The number of combinations of n objects taken r at a time is the quotient of and (n – r)! * r! n!

Combinations The students of Mr. Swift’s Seminar class had to choose 4 out of the 7 people who were nominated to serve on the Student Council. How many different groups of students could be selected?

Permutations and Combinations The students of Mr. Swift’s Seminar class had to choose 4 out of the 7 people who were nominated to serve on the Student Council. Question: How many different groups of students could be selected? The order in which the students are chosen does not matter, so this situation represents a combination of 7 people taken 4 at a time.

Permutations and Combinations The students of Mr. Fant’s Seminar class had to choose 4 out of the 7 people who were nominated to serve on the Student Council. How many different groups of students could be selected? The order in which the students are chosen does not matter, so this situation represents a combination of 7 people taken 4 at a time.

Permutations and Combinations The students of Mr. Fant’s Seminar class had to choose 4 out of the 7 people who were nominated to serve on the Student Council. How many different groups of students could be selected? The order in which the students are chosen does not matter, so this situation represents a combination of 7 people taken 4 at a time. There are 35 different groups of students that could be selected.

Example 2 Thomas Jefferson Middle School track team has 6 runners available for the 4 - person relay event. How many different 4 – person teams can be chosen?

Example 3 Our class is voting for new school colors. You are asked to choose 2 colors from a list of 8 colors. How many possibilities are there?

Probability Circuit 1)Must show me your thinking. 2)Write the poster number in a rectangle next to your work for each problem. 3)At the end of the circuit list all of your poster numbers in order based on the order you went around the room.