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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4. Find the counting problem below: a. 4x5x6x...x1000 b. (50 10) c. (255) d. 25 5 e. 50 10
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.
ACTIVITY 1. Read and analyze each situation. Solve each problem using fundamental counting techniques. 1. In a class there are 26 boys and 10 girls. The teacher wants to select 1 boy and 1 girl to represent a competition. In how many ways can the teacher make this selection ? 2. Given 8 flags of different colors, how many different signals can be generated if a signal requires the use of two flags, one below the other ? 3. A person wants to buy one fountain pen, one and one pencil from a stationery shop. ball pen If there are 10 fountain pen varieties, 15 ball pen varieties and 4 pencil varieties, in how many ways can he select these articles ? 4. Fifteen students compete in a race. In how many ways first three prizes be given ? 5. From among the 42 teachers in a college, one principal, one vice-principal and the teacher-in charge are to be appointed. In how many ways this can be done ?
Suppose you are ordering a calzone from D.P. Dough. You want 7 distinct toppings, chosen from their list of 13 vegetarian toppings. How many choices do you have for your calzone? Preview How many choices do you have for your calzone if you refuse to have green pepper as one of your toppings? Preview How many choices do you have for your calzone if you insist on having green pepper as one of your toppings? Preview