A teacher has 21 students, and 4 of them will be chosen to participate in a play that has 4 distinct characters. Which of the following questions requires calculating permutations to solve? Explain your reasoning. A) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are not distinct, the order of the children does not matter. B) How many different sets of 4 children can be selected for the play? When answering this question, the order of the children in the set matters. C) How many different sets of 4 children can be selected for the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found. D) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are distinct, the order of the children matters. E) How many different choices are possible for each role in the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found.
A teacher has 21 students, and 4 of them will be chosen to participate in a play that has 4 distinct characters. Which of the following questions requires calculating permutations to solve? Explain your reasoning. A) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are not distinct, the order of the children does not matter. B) How many different sets of 4 children can be selected for the play? When answering this question, the order of the children in the set matters. C) How many different sets of 4 children can be selected for the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found. D) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are distinct, the order of the children matters. E) How many different choices are possible for each role in the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 36SE: The number of 5-element subsets from a set containing n elements is equal to the number of 6-element...
Related questions
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, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Topic Video
Question
A teacher has 21 students, and 4 of them will be chosen to participate in a play that has 4 distinct characters. Which of the following questions requires calculating permutations to solve? Explain your reasoning.
A) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are not distinct, the order of the children does not matter.
B) How many different sets of 4 children can be selected for the play? When answering this question, the order of the children in the set matters.
C) How many different sets of 4 children can be selected for the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found.
D) Once the 4 children have been chosen, how many different ways can their roles be arranged? To answer this question, the total number of possible arrangements, or permutations, needs to be found. Since the roles are distinct, the order of the children matters.
E) How many different choices are possible for each role in the play? To answer this question, the total number of possible arrangements, or permutations, needs to be found.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning