I have recently developed an interest in the English Premier League and would like to plan atrip to see some of the stadiums the teams play in. There are 20 teams and each of them have asingle, unique stadium.(a) Suppose I want to visit 5 stadiums on my trip. How many sets of 5 stadiums are there forme to choose from?(b) Having done more research, I decide that I would like to visit 2 stadiums in London, 1 inWest Midlands, and 2 elsewhere. In total, there are 6 stadiums in London, 3 in WestMidlands, and 11 elsewhere. In how many ways can I choose a group of 5 stadiums that meetmy constraints? Describe howyouarrived at your solution.(c) Due to the pandemic, I won't be able to take this trip for a few years, at which pointManchester United (whose original stadium was one of the 11 elsewhere) have built a secondstadium in London to capitalize on being the most popular team in England. If I want tobe sure to see exactly one Manchester United stadium (both stadiums are too many, neitherstadium is too few), how many groups of 5 stadiums can I choose from? Note the constraintsfrom part b still apply as well. Describe how you arrived at your solution.

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Description: I have recently developed an interest in the English Premier League and would like to plan atrip to see some of the stadiums the teams play in. There are 20 teams and each of them have asingle, unique stadium.(a) Suppose I want to visit 5 stadiums o

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I have recently developed an interest in the English Premier League and would like to plan trip to see some of the stadiums the teams play in. There are 20 teams and each of them have single, unique stadium. (a) Suppose I want to visit 5 stadiums on my trip. How many sets of 5 stadiums are there for me to choose from? (b) Having done more research, I decide that I would like to visit 2 stadiums in London, 1 i West Midlands, and 2 elsewhere. In total, there are 6 stadiums in London, 3 in Wes Midlands, and 11 elsewhere. In how many ways can I choose a group of 5 stadiums that mee my constraints? Describe how you arrived at your solution. (c) Due to the pandemic, I won't be able to take this trip for a few years, at which poin Manchester United (whose original stadium was one of the 11 elsewhere) have built a second stadium in London to capitalize on being the most popular team in England. If I want to be sure to see exactly one Manchester United stadium (both stadiums are too many, neithe stadium is too few), how many groups of 5 stadiums can I choose from? Note the constraint from part b still apply as well. Describe how you arrived at your solution.

I have recently developed an interest in the English Premier League and would like to plan trip to see some of the stadiums the teams play in. There are 20 teams and each of them have single, unique stadium. (a) Suppose I want to visit 5 stadiums on my trip. How many sets of 5 stadiums are there for me to choose from? (b) Having done more research, I decide that I would like to visit 2 stadiums in London, 1 i West Midlands, and 2 elsewhere. In total, there are 6 stadiums in London, 3 in Wes Midlands, and 11 elsewhere. In how many ways can I choose a group of 5 stadiums that mee my constraints? Describe how you arrived at your solution. (c) Due to the pandemic, I won't be able to take this trip for a few years, at which poin Manchester United (whose original stadium was one of the 11 elsewhere) have built a second stadium in London to capitalize on being the most popular team in England. If I want to be sure to see exactly one Manchester United stadium (both stadiums are too many, neithe stadium is too few), how many groups of 5 stadiums can I choose from? Note the constraint from part b still apply as well. Describe how you arrived at your solution.

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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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

I have recently developed an interest in the English Premier League and would like to plan a
trip to see some of the stadiums the teams play in. There are 20 teams and each of them have a
single, unique stadium.
(a) Suppose I want to visit 5 stadiums on my trip. How many sets of 5 stadiums are there for
me to choose from?
(b) Having done more research, I decide that I would like to visit 2 stadiums in London, 1 in
West Midlands, and 2 elsewhere. In total, there are 6 stadiums in London, 3 in West
Midlands, and 11 elsewhere. In how many ways can I choose a group of 5 stadiums that meet
my constraints? Describe how
you
arrived at your solution.
(c) Due to the pandemic, I won't be able to take this trip for a few years, at which point
Manchester United (whose original stadium was one of the 11 elsewhere) have built a second
stadium in London to capitalize on being the most popular team in England. If I want to
be sure to see exactly one Manchester United stadium (both stadiums are too many, neither
stadium is too few), how many groups of 5 stadiums can I choose from? Note the constraints
from part b still apply as well. Describe how you arrived at your solution.

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