Lightning Round. Decide if the following use the Fundamental Counting Principle, Permutation, or Combination and then solve. a. Planting 5 out of 12 plants in the garden. b. Choosing a President and Vice President from a group of 10 candidates. c. From 10 pizza toppings, picking 3. d. Pizza combinations – how many possible choices would you have if you had to choose between thick or thin crust, red or white sauce, and a single topping from 12 possible choices? e. The number of possible choices if you had Pepsi, Diet Pepsi, or Mountain Dew in cans or bottles. f. Choosing a committee of 4 from 56 people. g. Selecting the starting baseball lineup of 9 players from 15 teammates (order matters). h. Possible 5 card poker hands from a standard deck of cards (52 cards). i. From a class of 25 students, 3

Lightning Round. Decide if the following use the Fundamental Counting Principle, Permutation, or Combination and then solve. a. Planting 5 out of 12 plants in the garden. b. Choosing a President and Vice President from a group of 10 candidates. c. From 10 pizza toppings, picking 3. d. Pizza combinations – how many possible choices would you have if you had to choose between thick or thin crust, red or white sauce, and a single topping from 12 possible choices? e. The number of possible choices if you had Pepsi, Diet Pepsi, or Mountain Dew in cans or bottles. f. Choosing a committee of 4 from 56 people. g. Selecting the starting baseball lineup of 9 players from 15 teammates (order matters). h. Possible 5 card poker hands from a standard deck of cards (52 cards). i. From a class of 25 students, 3

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question: In the entrepreneur project competition. You are chief guest of the competition and you have to pickthe top 4 paintings out of 10. Since the order is important. In how many different ways of picking the top three entrepreneur projects.
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4. Find the counting problem below: a. 4x5x6x...x1000 b. (50 10) c. (255) d. 25 5 e. 50 10
Tyler was given the following counting problem to solve: “ You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one queen and at least one spade. He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades QA. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four cards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queen spade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades so that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes that the answer is 51C4 + (3 · 12 · 49C3). His answer is incorrect. Explain why, and give the correct answer.
Tyler was given the followng counting problem to solve: " You are dealt five cards from a standard deck 52 cards. How many of these hands have at least one queen and at least one spade." He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four cards. In the second case, he will start by choosing a non-spade queen ( 3 ways) and a non-queen spade (12 ways). There are 50 cards remaning, so he also throws away the Queen of Spades so that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes that the answer is 51C4 + (3 x 12 x 49C3). His answer is wrong, explain why and give the correct answer.
Analyze the given problem if it's permutation, combination, factorial or fundamental. Provide a clear solution.
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Topic: Solving Problems involving Permutations. Solve the problems completely. Show your solution In how many ways can 5 people sit at a round table if:a. they may sit anywhere?b. two insist on sitting beside each other?c. three refuse to sit beside each other?