(a) A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is (b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let 7 be the set of all possible selections, assuming that there are at least 28 balloons of each type, let R ≤12 be the set of selections in 7 that contain 12 or fewer red balloons, and let R≥13 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and 7 to find that the number of different combinations of 28 balloons that can be chosen is (c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
(a) A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is (b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let 7 be the set of all possible selections, assuming that there are at least 28 balloons of each type, let R ≤12 be the set of selections in 7 that contain 12 or fewer red balloons, and let R≥13 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and 7 to find that the number of different combinations of 28 balloons that can be chosen is (c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
Related questions
Question
need help
Transcribed Image Text:(a) A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?
Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is
(b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question.
If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let 7 be the set of all possible selections, assuming that there are at least 28 balloons of each
type, let R ≤12 be the set of selections in 7 that contain 12 or fewer red balloons, and let R≥13 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and 7 to find that the number of different combinations of 28 balloons that can be chosen is
(c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
(d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
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 5 images
Recommended textbooks for you
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL