If Larry, Moe and Curly visit a town with 7 churches
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I am working through the following question:
If Larry, Moe and Curly visit a town with 7 churches, then (a) in how many ways can all three visit the same church, and (b) in how many ways will they not all choose the same church?
For a) I have the following calculation:
$$binom{7}{1} = 7$$
Is it that simple or am I missing something?
For b) I have this:
$$P_3^7 = 210$$
Am I on the right path, or have I made any errors? Thanks for your help!
permutations combinations
asked Nov 20 at 7:49
Lee
1015
add a comment |
up vote
2
down vote
favorite
I am working through the following question:
If Larry, Moe and Curly visit a town with 7 churches, then (a) in how many ways can all three visit the same church, and (b) in how many ways will they not all choose the same church?
For a) I have the following calculation:
$$binom{7}{1} = 7$$
Is it that simple or am I missing something?
For b) I have this:
$$P_3^7 = 210$$
Am I on the right path, or have I made any errors? Thanks for your help!
permutations combinations
asked Nov 20 at 7:49
Lee
1015
3
a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I am working through the following question:
If Larry, Moe and Curly visit a town with 7 churches, then (a) in how many ways can all three visit the same church, and (b) in how many ways will they not all choose the same church?
For a) I have the following calculation:
$$binom{7}{1} = 7$$
Is it that simple or am I missing something?
For b) I have this:
$$P_3^7 = 210$$
Am I on the right path, or have I made any errors? Thanks for your help!
permutations combinations
asked Nov 20 at 7:49
Lee
1015
I am working through the following question:
If Larry, Moe and Curly visit a town with 7 churches, then (a) in how many ways can all three visit the same church, and (b) in how many ways will they not all choose the same church?
For a) I have the following calculation:
$$binom{7}{1} = 7$$
Is it that simple or am I missing something?
For b) I have this:
$$P_3^7 = 210$$
Am I on the right path, or have I made any errors? Thanks for your help!
permutations combinations
permutations combinations
asked Nov 20 at 7:49
Lee
1015
asked Nov 20 at 7:49
Lee
1015
asked Nov 20 at 7:49
Lee
1015
asked Nov 20 at 7:49
Lee
1015
asked Nov 20 at 7:49
Lee
1015
1015
3
a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49
add a comment |
3
a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49
3
3
a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49
add a comment |
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a) Yep. Right. And for b), just realize that the number of ways they will not all choose the same church is the total number of ways they can go to church minus the number of ways they all go to the same church. Easy!
– David G. Stork
Nov 20 at 7:52
@DavidG.Stork Thank you! That clears things up!
– Lee
Nov 20 at 8:00
Larry, Moe, and Curly were all Jewish (archive.jns.org/latest-articles/2012/12/3/…), so they were probably visiting synagogues rather than churches. Anyway, the answers depend on whether or not Larry visiting a given house of worship followed by Moe is considered different from Moe visiting first, followed by Larry, and so on.
– Gerry Myerson
Nov 20 at 8:25
Your answer on b) actually answers another question: "in how many ways can they all choose a different church to visit?"
– drhab
Nov 20 at 9:49