(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 98,280 (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 T 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 R213 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R213, and 7 to find that the number of different combinations of 28 balloons that can be chosen is 196,560 x (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? 0 × (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? 78,652 ×
(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 98,280 (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 T 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 R213 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R213, and 7 to find that the number of different combinations of 28 balloons that can be chosen is 196,560 x (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? 0 × (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? 78,652 ×
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.1: Counting
Problem 92E: DISCUSS: Complementary Combinations Without performing any calculations, explain in words Why the...
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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 98,280
(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 T 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 R213 be the set of selections from 7 that contain 13 or more red balloons. Use the relationships among R≤12, R213, and 7 to find that the number of different combinations of 28 balloons that can be chosen is
196,560
x
(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?
0
×
(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?
78,652
×
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