Problem 3. How many ways are there to select an 11-member soccer team and a 5-memberbasketball team from a class of 30 students if(1) nobody can be on both teams.(2) any number of students can be on both the teams.(3) at most one student can be on both the teams.

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Answered: Problem 3. How many ways are there to…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider a 6 vs 6 youth soccer team (i.e., teams field 6 players at once) with 9 players. (a) How many different combinations of players can the team field? (b) If the team has exactly one goalie (who has to play), how many different combinations of players can the team field? (c) If the team has exactly two goalie (exactly one of which has to play and the other cannot), how many different combinations of players can the team field?
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For this problem, assume the cooler contains 28 cans, 10 of which are regular, and the rest of which are diet. (1) How many ways can you choose 5 cans from the cooler? (2) How many ways can you choose 5 regular cans from the cooler? (3) How many ways can you choose 5 diet cans from the cooler? (4) How many ways can you choose 5 cans from the cooler so that at least 4 are diet?

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Problem 3. How many ways are there to select an 11-member soccer team and a 5-member basketball team from a class of 30 students if (1) nobody can be on both teams. (2) any number of students can be on both the teams. (3) at most one student can be on both the teams.