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Permutations and Combinations

Permutations and Combinations. Lesson 6-7. Additional Examples. In how many ways can 6 people line up from left to right for a group photo?. Since everybody will be in the picture, you are using all the items from the original set. You can use the Multiplication Counting Principle or

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Permutations and Combinations

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  1. Permutations and Combinations Lesson 6-7 Additional Examples In how many ways can 6 people line up from left to right for a group photo? Since everybody will be in the picture, you are using all the items from the original set. You can use the Multiplication Counting Principle or factorial notation. There are six ways to select the first person in line, five ways to select the next person, and so on. The total number of permutations is 6 • 5 • 4 • 3 • 2 • 1 = 6!. 6! = 720 The 6 people can line up in 720 different orders.

  2. 26! (26 – 4)! 26! 22! 26P4 = = = 358,800 Permutations and Combinations Lesson 6-7 Additional Examples How many 4-letter codes can be made if no letter can be used twice? Method 1: Use the Multiplication Counting Principle. 26 • 25 • 24 • 23 = 358,800 Method 2: Use the permutation formula. Since there are 26 letters arranged 4 at a time, n = 26 and r = 4. There are 358,800 possible arrangements of 4-letter codes with no duplicates.

  3. 10! 4!(10 – 4)! 10C4 = 10! 4! • 6! = 1 2 3 6 5 4 4 3 1 6 2 5 10 • 9 • 8 • 7 • 4 • 3 • 2 • 1 • • • • • • = • • • • • 10 • 9 • 8 • 7 4 • 3 • 2 • 1 = Permutations and Combinations Lesson 6-7 Additional Examples Evaluate 10C4. = 210

  4. Relate: 12 songs chosen 5 songs at a time Define: Let n = total number of songs. Let r = number of songs chosen at a time. Write:nCr = Use the nCrfeature of your calculator. 12C5 Permutations and Combinations Lesson 6-7 Additional Examples A disk jockey wants to select 5 songs from a new CD that contains 12 songs. How many 5-song selections are possible? You can choose five songs in 792 ways.

  5. You may choose  4 toppings, 3 toppings, 2 toppings, 1 toppings, or none. 9C49C39C29C19C0 Permutations and Combinations Lesson 6-7 Additional Examples A pizza menu allows you to select 4 toppings at no extra charge from a list of 9 possible toppings. In how many ways can you select 4 or fewer toppings? The total number of ways to pick the toppings is 126 + 84 + 36 + 9 + 1 = 256. There are 256 ways to order your pizza.

  6. http://youtu.be/1stIqr0FGiE https://youtu.be/PSS3mCS_Ef8

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