College

We appreciate your visit to For each situation determine whether to use a permutation or a combination Then solve the problem 16 How many different orders can you choose to. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

For each situation, determine whether to use a permutation or a combination. Then, solve the problem.

16. How many different orders can you choose to read six of nine books on your summer reading list?

17. How many ways are there to choose five shirts out of seven to take to camp?

18. How many ways can you choose two out of four kinds of flowers to put in a bouquet?

19. How many five-person committees can be made from a group of twelve people?

20. From a group of 6 seniors and 8 juniors, how many ways can 3 seniors and 2 juniors be chosen?

21. You must answer exactly 12 out of 15 multiple-choice questions on a test. How many different ways can you select the questions to answer?

22. A lab assigns a three-digit identification code to each subject in an experiment. No two subjects have the same identification, and no digit can be repeated in an identification code. What is the greatest number of subjects that can be used in the experiment?

23. To mark its eighth anniversary, Pizzeria Otto has a special coupon that offers the same price on a pizza with any combination of the 8 original toppings. Each pizza must have at least one topping. How many different kinds of pizza can be ordered with the coupon?

Answer :

Final answer:

The problems require determining whether to use combinations or permutations based on whether the order of selection matters. Examples show how to calculate the number of ways to select items in various scenarios, leading to correct total values for each situation.


Explanation:

Analysis of Combinations and Permutations

In this set of problems, we determine whether to use permutations or combinations based on the context of the question. A permutation is used when the order of selection matters, while a combination is used when the order does not matter.

  1. Problem 16: Different Orders of Reading Books

    Since the order in which you read the books matters, we use permutations. The number of permutations of selecting 6 books from 9 is calculated as: P(9, 6) = 9! / (9-6)! = 9! / 3! = 9 × 8 × 7 × 6 × 5 × 4 = 60480.

  2. Problem 17: Choosing Shirts

    Here, the order does not matter, so we use combinations. The number of combinations to choose 5 shirts out of 7 is calculated as: C(7, 5) = 7! / [5! × (7-5)!] = 21.

  3. Problem 18: Choosing Flowers

    Similar to the previous problem, order does not matter, so we use combinations. The number of ways to choose 2 out of 4 flowers is: C(4, 2) = 4! / [2! × (4-2)!] = 6.

  4. Problem 19: Five-Person Committees

    Again, the order does not matter, leading us to use combinations. The number of 5-person committees from a group of 12 people is: C(12, 5) = 792.

  5. Problem 20: Seniors and Juniors

    Since the order does not matter, we apply combinations. The number of ways to choose 3 seniors from 6 and 2 juniors from 8 is given by: C(6, 3) × C(8, 2) = 20 × 28 = 560.

  6. Problem 21: Choosing Multiple Choice Questions

    Here, the order does not matter, so we use combinations. The number of ways to select 12 questions out of 15 is: C(15, 12) = C(15, 3) = 455.

  7. Problem 22: Three-Digit Identification Code

    Since no digit can be repeated, the order matters, thus we use permutations. The greatest number of subjects that can be coded is: P(10, 3) = 10 × 9 × 8 = 720.

  8. Problem 23: Pizzeria Otto's Toppings

    This is a combination problem because the order of toppings does not matter, and pizzas must have at least one topping. The total combinations can be calculated using the formula: 2^8 - 1 = 255, where 2^8 represents all combinations including no toppings.


Learn more about Combinations and Permutations here:

https://brainly.com/question/3901018


Thanks for taking the time to read For each situation determine whether to use a permutation or a combination Then solve the problem 16 How many different orders can you choose to. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada