How many ways letters be placed so at least two of them are in wrong envelopes? [duplicate]
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How many fixed points in a permutation
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A person writes letters to six friends and their addresses to corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?
combinatorics discrete-mathematics
edited Sep 7 at 10:26
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This question already has an answer here:
How many fixed points in a permutation
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A person writes letters to six friends and their addresses to corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?
combinatorics discrete-mathematics
edited Sep 7 at 10:26
N. F. Taussig
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asked Sep 7 at 10:15
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6
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
2
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53
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up vote
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This question already has an answer here:
How many fixed points in a permutation
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A person writes letters to six friends and their addresses to corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?
combinatorics discrete-mathematics
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
asked Sep 7 at 10:15
user9640947
366
This question already has an answer here:
How many fixed points in a permutation
2 answers
A person writes letters to six friends and their addresses to corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in wrong envelopes?
This question already has an answer here:
How many fixed points in a permutation
2 answers
combinatorics discrete-mathematics
combinatorics discrete-mathematics
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
asked Sep 7 at 10:15
user9640947
366
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
asked Sep 7 at 10:15
user9640947
366
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
edited Sep 7 at 10:26
N. F. Taussig
39.7k93153
39.7k93153
asked Sep 7 at 10:15
user9640947
366
asked Sep 7 at 10:15
user9640947
366
asked Sep 7 at 10:15
user9640947
366
366
marked as duplicate by Peter Taylor, Jendrik Stelzner, amWhy discrete-mathematics
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This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
6
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
2
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53
add a comment |Â
6
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
2
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53
6
6
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
2
2
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53
add a comment |Â
1 Answer
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If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)
answered Sep 7 at 11:15
MRobinson
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)
answered Sep 7 at 11:15
MRobinson
74015
add a comment |Â
up vote
4
down vote
accepted
If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)
answered Sep 7 at 11:15
MRobinson
74015
add a comment |Â
up vote
4
down vote
accepted
up vote
4
down vote
accepted
If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)
answered Sep 7 at 11:15
MRobinson
74015
If the person is placing the letters in the envelopes at random, and the order matters, there will be $6! = 720$ ways of placing the letters, and only of those has all of the letters placed correctly. So there are $719$ ways of making a mistake. (Note that one mistake means at least 2 are incorrect)
answered Sep 7 at 11:15
MRobinson
74015
answered Sep 7 at 11:15
MRobinson
74015
answered Sep 7 at 11:15
MRobinson
74015
answered Sep 7 at 11:15
MRobinson
74015
74015
add a comment |Â
add a comment |Â
6
Note: you can never have only $1$ letter in the wrong envelope.
– Mohammad Zuhair Khan
Sep 7 at 10:20
2
@MohammadZuhairKhan - you can if one envelope is empty and another contains two letters, though this question probably assumes each envelope contains exactly one letter
– Henry
Sep 7 at 10:53