Probability: $12$ questions $12$ answers to be matched
There are $12$ questions and $12$ answers on a test. Assuming each answer can only be matched to $1$ question, what is the probability of getting $4$ correct matching randomly and how would you calculate this?
probability
edited Nov 20 at 11:39
idea
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
add a comment |
There are $12$ questions and $12$ answers on a test. Assuming each answer can only be matched to $1$ question, what is the probability of getting $4$ correct matching randomly and how would you calculate this?
probability
edited Nov 20 at 11:39
idea
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
1
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35
add a comment |
There are $12$ questions and $12$ answers on a test. Assuming each answer can only be matched to $1$ question, what is the probability of getting $4$ correct matching randomly and how would you calculate this?
probability
edited Nov 20 at 11:39
idea
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
There are $12$ questions and $12$ answers on a test. Assuming each answer can only be matched to $1$ question, what is the probability of getting $4$ correct matching randomly and how would you calculate this?
probability
probability
edited Nov 20 at 11:39
idea
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
edited Nov 20 at 11:39
idea
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
edited Nov 20 at 11:39
idea
2,16841024
edited Nov 20 at 11:39
idea
2,16841024
edited Nov 20 at 11:39
idea
2,16841024
2,16841024
asked Nov 20 at 11:30
Tee Lee
6
asked Nov 20 at 11:30
Tee Lee
6
asked Nov 20 at 11:30
Tee Lee
6
6
Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
1
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35
add a comment |
Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
1
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35
Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
1
1
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35
add a comment |
1 Answer
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Hint:
Select $4$ questions to be matched with $4$ corresponding answers, in $^{12}C_4$ ways.
And ensure that rest $8$ questions are matched with any, but not their correct answers.
This is done using De-arrangement of $8$, i.e. $D_8$.
Total possible arrangements are obviously $12!$.
edited Nov 20 at 11:54
Especially Lime
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
add a comment |
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1 Answer
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1 Answer
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Hint:
Select $4$ questions to be matched with $4$ corresponding answers, in $^{12}C_4$ ways.
And ensure that rest $8$ questions are matched with any, but not their correct answers.
This is done using De-arrangement of $8$, i.e. $D_8$.
Total possible arrangements are obviously $12!$.
edited Nov 20 at 11:54
Especially Lime
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
add a comment |
Hint:
Select $4$ questions to be matched with $4$ corresponding answers, in $^{12}C_4$ ways.
And ensure that rest $8$ questions are matched with any, but not their correct answers.
This is done using De-arrangement of $8$, i.e. $D_8$.
Total possible arrangements are obviously $12!$.
edited Nov 20 at 11:54
Especially Lime
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
add a comment |
Hint:
Select $4$ questions to be matched with $4$ corresponding answers, in $^{12}C_4$ ways.
And ensure that rest $8$ questions are matched with any, but not their correct answers.
This is done using De-arrangement of $8$, i.e. $D_8$.
Total possible arrangements are obviously $12!$.
edited Nov 20 at 11:54
Especially Lime
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
Hint:
Select $4$ questions to be matched with $4$ corresponding answers, in $^{12}C_4$ ways.
And ensure that rest $8$ questions are matched with any, but not their correct answers.
This is done using De-arrangement of $8$, i.e. $D_8$.
Total possible arrangements are obviously $12!$.
edited Nov 20 at 11:54
Especially Lime
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
edited Nov 20 at 11:54
Especially Lime
21.6k22858
edited Nov 20 at 11:54
Especially Lime
21.6k22858
edited Nov 20 at 11:54
Especially Lime
21.6k22858
21.6k22858
answered Nov 20 at 11:45
idea
2,16841024
answered Nov 20 at 11:45
idea
2,16841024
answered Nov 20 at 11:45
idea
2,16841024
2,16841024
add a comment |
add a comment |
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Is it EXACTLY four or at least four? I would first consider all the possible options ($12!$) and see how many cases there are that fulfill the requirement.
– Matti P.
Nov 20 at 11:34
1
Hint: you'll want to use Derangements.
– lulu
Nov 20 at 11:35