probability of getting corrct clothes in dry cleaning

ketanco

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a dry cleaner gives 4 identical shirts randomly to 4 people, where each person owns one shirt. what is the probability of at least one person getting his own shirt?

the answer is 175 / 256

i figured out the 256, which is the total number of situations, which is 4^4

i just can not figure out how we get 175
 
a dry cleaner gives 4 identical shirts randomly to 4 people, where each person owns one shirt. what is the probability of at least one person getting his own shirt?

the answer is 175 / 256

i figured out the 256, which is the total number of situations, which is 4^4

i just can not figure out how we get 175

Derangements are fun! P(At Least One) = p(1, 2, 3, or 4) = 1 - P(None)

Really though, not a fan of this problem statement or the given answer. Were the four shirts originally owned by the four individuals or did the Dry Cleaner just pull four shirts off the rotating rack? Each owns one shirt, sure, but is the shirt owned actually among the four selected? Also, why do they have to be identical? Further, there are only 9 derangements among the 24 permutations of a 4-element set.
 
Derangements are fun! P(At Least One) = p(1, 2, 3, or 4) = 1 - P(None)

Really though, not a fan of this problem statement or the given answer. Were the four shirts originally owned by the four individuals or did the Dry Cleaner just pull four shirts off the rotating rack? Each owns one shirt, sure, but is the shirt owned actually among the four selected? Also, why do they have to be identical? Further, there are only 9 derangements among the 24 permutations of a 4-element set.

I think your questions are irrelevant. The question is giving enough information.

Not that it will improve solving qyestion bit justvto answer you, yes they are owned by those 4 people as stated in the question. Yes, being identical helps to state thatthey are given randomly.
 
a dry cleaner gives 4 identical shirts randomly to 4 people, where each person owns one shirt. what is the probability of at least one person getting his own shirt?
the answer is 175 / 256
i figured out the 256, which is the total number of situations, which is 4^4
i just can not figure out how we get 175
As stated the question is hard to read despite what you say.
That given answer is total nonsense.
The correct answer is \(\displaystyle 1-\dfrac{\mathscr{D} _ 4 }{4!}=1-\dfrac{9}{24}=\dfrac{5}{8}\)

BTW you could use some help in English composition.
 
the answer i gave is the correct one.What you write is wrong.

first of all the total possible situations are 4^4 and 256 is right from the start....

About english... It is enough to tell what i want here...and i gave enough facts in the question, without leaving space for the irrelevant questions you asked. How many languages do you speak? I speak 5.

I gave enough facts in the question.
 
a dry cleaner gives 4 identical shirts randomly to 4 people, where each person owns one shirt. what is the probability of at least one person getting his own shirt?

the answer is 175 / 256

i figured out the 256, which is the total number of situations, which is 4^4

i just can not figure out how we get 175

4^4 would be the correct denominator if the same shirt could be given to more than one person. This is a permutation situation, where each can only be given once. The denominator has to be 4! = 24.

Why do you say 256 is correct? Where did the problem, and the supposed solution, come from? Have you learned anything about derangements? What topics have you covered, that this might be intended to be an exercise in?

Possibly we are misunderstanding the problem, though it seems reasonably clear to me.
 
4^4 would be the correct denominator if the same shirt could be given to more than one person. This is a permutation situation, where each can only be given once. The denominator has to be 4! = 24.

Why do you say 256 is correct? Where did the problem, and the supposed solution, come from? Have you learned anything about derangements? What topics have you covered, that this might be intended to be an exercise in?

Possibly we are misunderstanding the problem, though it seems reasonably clear to me.

people are different but shirts are identical. it is like tossing a coin 4 times. how many situations are there? 2^4 outcomes (two possibilities for a coin)

i saw 175 / 256 as the answer. this is all i can say sorry... i am just solving tests for a general exam in Maths...

by saying 4!, arent you dictating a certain shirt must be given out first? but all 4 can be given out to all 4 people first... though that way the solution should be 4x4 x 3x3 x 2x2 x 1x1 = 576 for total situations...
 
people are different but shirts are identical. it is like tossing a coin 4 times. how many situations are there? 2^4 outcomes (two possibilities for a coin)
i saw 175 / 256 as the answer. this is all i can say sorry... i am just solving tests for a general exam in Maths...
by saying 4!, arent you dictating a certain shirt must be given out first? but all 4 can be given out to all 4 people first... though that way the solution should be 4x4 x 3x3 x 2x2 x 1x1 = 576 for total situations...
That is nonsensical. If the shirts are identical it makes no to ask if a person get his own shirt? How would he know.
If you say that the shirts are tagged then they are no longer identical.
In your example, flipping a coin, the coin is identical.
 
That is nonsensical. If the shirts are identical it makes no to ask if a person get his own shirt? How would he know.
If you say that the shirts are tagged then they are no longer identical.
In your example, flipping a coin, the coin is identical.
sorry that the preparers prepared the question that way... but that is the question... shirts are identical.... each one is owned by one of four people....
 
sorry that the preparers prepared the question that way... but that is the question... shirts are identical.... each one is owned by one of four people....
O.K. Lets clean it up. There are four shirts that are identical in every way except the owner name in inked in the collar. After laundering the shirts are put on hangers in such a way as to cause the names to be hidden. So each of the four men randomly grabs a shirt off the rack. What is the probability that at least one man gets his own shirt? We need to know about derangement. \(\displaystyle \mathscr{D} _ n =\left\lfloor {\dfrac{n!}{e}+\dfrac{1}{2}} \right\rfloor \)

The correct answer is \(\displaystyle 1-\dfrac{\mathscr{D} _ 4 }{4!}=1-\dfrac{9}{24}=\dfrac{5}{8}\)
 
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though that way the solution should be 4x4 x 3x3 x 2x2 x 1x1 = 576 for total situations...

One thing that will help you get through some maths is an open mind. LISTEN to your forebears. Feel free to believe that the question or the given answer might be wrong.

#1 This is a STANDARD permutation problem. Nothing new or fancy about it. If the author wants otherwise, said author has failed to state it.
First Shirt can be awarded to any of the 4 individuals. This leaves only three candidates for the second shirt.
Second Shirt can be awarded to any of the 3 remaining individuals. This leaves only two candidates for the third shirt.
etc.

We aren't taking back the shirts after awarding them. There are 4! = 24 permutations. If we're giving one shirt to each, that's it. If the author of the question INSISTS that the denominator is 256, and IF the author is correct, then the author simply has worded the question incorrectly. Possibly, it has been translated very poorly.

Time to let go of the preposterous and actually think about the problem statement. This is what makes my questions relevant. They call into question the problem statement itself - which thing needs to be done.

So, rather than insisting that a higher heavenly power has written, solved, and translated the problem statement, let's see what we can think on the matter?


My views. I welcome others'.
 
O.K. Lets clean it up. There are four shirts that are identical in every way except the owner name in inked in the collar. After laundering the shirts are put on hangers in such a way as to cause the names to be hidden. So each of the four men randomly grabs a shirt off the rack. What is the probability that at least one man gets his own shirt? We need to know about derangement. \(\displaystyle \mathscr{D} _ n =\left\lfloor {\dfrac{n!}{e}+\dfrac{1}{2}} \right\rfloor \)

The correct answer is \(\displaystyle 1-\dfrac{\mathscr{D} _ 4 }{4!}=1-\dfrac{9}{24}=\dfrac{5}{8}\)

you wrote your own question... and solved it... well done.... but your question unfortunately is different than mine....
the dry cleaning shop owner RANDOMLY gives shirts. shirts are identical. no tagging.... no hanging.... no coloring.... those are done in your version... not mine....

may be they wrote the question wrong... or the answer is wrong.. but these are what I saw in study notes... and yes i translated it well enough.... nothing is lost in translation.... i assure you of that....

so if the question or question plus answer makes no sense, then it makes no sense... i will not insist on a question someone else wrote... this was the question... thanks for the efforts.....
 
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you wrote your own question... which is different than mine....
Yes I did. Because your question is utter nonsense. It has no answer. The shirts cannot be identical in every way and yet be identified by its owner.
 
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