Explanation Given Information: A bag contains four red marbles, 2 green, 1 transparent, 3 yellow and 2 orange. Formula used: The Decision Algorithm is to make a set of decisions to determine the number of possible outcomes. The Multiplication Principle is, if there is a sequence of choice with r disjoint steps and step 1 has n 1 possible outcomes, step 2 has n 2 possible outcomes and so on and step r has n r possible outcomes with no two outcomes same, then the total number of outcomes are n 1 × n 2 × … × n r . A combination of n items taken r at a time is an unordered list and the number of combinations is C ( n , r ) = n × ( n − 1 ) × … × ( n − r + 1 ) r ! . The Addition Principle is, if there is a choice among r disjoint alternatives and alternative 1 has n 1 possible outcomes, alternative 2 has n 2 possible outcomes and so on and alternative r has n r possible outcomes with no two outcomes same, then the total number of outcomes are n 1 + n 2 + … + n r . Calculation: Consider a bag contains 4 red marbles, 2 green, 1 transparent, 3 yellow and 2 orange. Thus, the total number of marbles in the bag is 12 . Consider there are 3 yellow marbles. Thus, there are 12 − 3 = 9 non-yellow marbles. Consider there are 4 red marbles. Thus, there are 12 − 4 = 8 non-red marbles. Use the Decision Algorithm to make a set of decisions to determine the number of possible outcomes. Consider the Decision Algorithm, there are 5 empty slots and choose at most 1 of the red marbles but no yellow ones. Alternative 1: choose 0 red marble. Step 1: Choose 5 non-red and non-yellow marbles. Since, there are 5 non-red, non-yellow marbles and 5 to choose. Thus, Step 1 has C ( 5 , 5 ) choices. Alternative 2: choose 1 red marble. Step 1: Choose 1 red marbles. Since, there are 4 red marbles and 1 to choose. Thus, Step 1 has C ( 4 , 1 ) choices. Step 2: Choose 4 non-red and non-yellow marbles. Since, there are 5 non-red, non-yellow marbles and 4 to choose. Thus, Step 2 has C ( 5 , 4 ) choices. Consider Alternative 1 has C ( 5 , 5 ) choices. Recall that a combination of n items taken r at a time is an unordered list and the number of combinations is C ( n , r ) = n × ( n − 1 ) × … × ( n − r + 1 ) r ! . Calculate C ( 5 , 5 ) . Substitute 5 for n and 5 for r in C ( n , r ) = n × ( n − 1 ) × … × ( n − r + 1 ) r ! . C ( 5 , 5 ) = 5 × ( 5 − 1 ) × … × ( 5 − 5 + 1 ) 5 ! = 5 × 4 × 3 × 2 × 1 5 × 4 × 3 × 2 × 1 = 1 Thus, Alternative 1 has 1 choice. Consider Alternative 2

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba…

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Videos

Question

Chapter 6, Problem 24RE

To determine

To calculate: The number possible sets of 5 marbles which include at most 1 of the red marbles but no yellow ones where a bag contains four red marbles, 2 green, 1 transparent, 3 yellow and 2 orange.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 23RE

Chapter 6, Problem 25RE

Students have asked these similar questions

A box contains 9 red, 8 blue, and 13 green balls of the same size. How many balls, do we need to take out (without looking) from the box to be sure that we have one ball of each colour?

In a rugby match,a tie at the end of two overtime periods leads to a "shootout" with five kicks taken by each team from the center of the 22-meter line. Each kick must be taken by a different player. How many ways can 5 players be selected from the 15 eligible players? For the 5 selected players, how many ways can they be designated as first, second, third, fourth, and fifth?

A fashion designer needs to design a new shirt. She has 7 different types of materials, 14 different colors for each material, and 9 different styles she can create. How many different shirts could the designer create using these parameters?

Chapter 6 Solutions

Finite Mathematics

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The number possible sets of 5 marbles which include at most 1 of the red marbles but no yellow ones where a bag contains four red marbles, 2 green, 1 transparent, 3 yellow and 2 orange.

Solution Summary: The author calculates the number of possible sets of 5 marbles, which include at most 1 red marble but no yellow ones.

Concept explainers

Videos

To calculate: The number possible sets of 5 marbles which include at most 1 of the red marbles but no yellow ones where a bag contains four red marbles, 2 green, 1 transparent, 3 yellow and 2 orange.

Want to see the full answer?

Chapter 6 Solutions