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Jacob has a lock that has 6 buttons numbered from 1 to 6. The lock is opened by pushing down 5 buttons at the same time. Unfortunately, Jacob has forgotten the correct combination to open the lock. If he randomly picks 5 buttons to push down, what is the probability that the lock can be opened?

Oct 7, 2018

#1
+99736
+2

The total number of possible  combinations  = C(6, 5)   =  6

So...the probabilty  is    1 /  6

Oct 7, 2018
edited by CPhill  Oct 8, 2018
edited by CPhill  Oct 8, 2018
#2
0

I think this should go something like this:

Total number of possible combinations, or rather, permutations of 6 numbers is: 6! =720

The number of ways of choosing 5 numbers out of 6 numbers is: 6C5 =6

Therefore, the probability of opening the Lock should be: 6/720 =1/120

Oct 7, 2018
#3
+18138
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Another look:

Possible combinations         1 2 3 4 5

2 3 4 5 6

1 3 4 5 6

1 2 4 5 6

1 2 3 5 6

Only SIX combintaions are possible since you push FIVE of the buttons down at ONCE

So you have a   1 out of 6 chance of getting it correct (as Cphil found)

Oct 7, 2018
#4
+99736
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EP..I actually think that the guest's answer is  somewhat correct.....here's why

lAlthough  it is true that there are only   6 diferent  combinations of numbers....sequencing is important....for instance

If the correct combination  is   5  4  1   3   6

This isn't the same as   1  3  4  5  6

So...for each combo....we can  permute them in   5! ways

So.....  6  * 5!   =   720

But only one of the selected sequences must be the correct one

So.....  1/ 720   seems to be the  correct answer   ???

CPhill  Oct 7, 2018
edited by CPhill  Oct 7, 2018
#10
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.....BUT it says that you push 5 buttons AT THE SAME TIME ....at ONCE, so there is no sequencing involved.....SO I think YOUR ANSWER is the correct one.    ~EP

ElectricPavlov  Oct 8, 2018
#11
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Yeah, EP....I finally realized that my first answer was correct....

[ Thanks for your reinforcement  ...LOL!! ]

CPhill  Oct 8, 2018
#12
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That is very fucking astute of you, EP!

Guest Oct 8, 2018
edited by Guest  Oct 8, 2018
#13
+18138
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Well.....  Thanx !      But really, it was nothing special compared to your insightful and thoughtful postings.....you add so much to the conversation, we could not do without you.

ElectricPavlov  Oct 8, 2018
#14
+100259
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LOL

Melody  Oct 8, 2018
#15
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Yes, that’s true.  Only a few have ever publicly recognized the thoughtful insights I’ve brought to the forum.  When this happens, it usually seems like they are stating the obvious. This is why I rarely self-aggrandize, because it seems like I’m stating the obvious.

Guest Oct 10, 2018
#16
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Are you able to recognize veiled sarcasm??!!

Guest Oct 10, 2018
#17
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"Are you able to recognize veiled sarcasm ??!!"

Yes. I can recognize veiled sarcasm.  It is obvious that you cannot –at least when there are two or more veils.

EP and Melody will probably recognize it. I know goddamnn well CPhill will recognize it. It’s near impossible for irony and sarcasm to escape Alfred E. Neuman.

For you and your brothers, though, there is no recognition. You're just too dumb!

Guest Oct 10, 2018
edited by Guest  Oct 10, 2018
edited by Guest  Oct 10, 2018
#18
0

Your words are as clear as a "Chimp's footprint in mud" !!.

Guest Oct 10, 2018
#19
+1409
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Mr. BB, the essence of your arrogant, mind-numbing dumbness and blarney permeates any environment you visit. You may have recognized a chimp, but there are no chimp footprints here. We chimps prefer to travel in trees, and we rarely leave footprints.

The big footprints belong to a gorilla. The small turkey footprints in the mud are yours, and the veiled and unveiled stupidity is yours and yours alone.

GA

GingerAle  Oct 11, 2018
#5
+575
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CPhill last answer is right.

The general formula for permutation is $$nPr=\frac{n!}{(n-r)!}$$

In this case $${6}^{P}{5}=\frac{6!}{(6-5)!}=720$$.possible combination,that is Jocab has 1/720 chance to open the lock at one time.

A rule of thumb to dealing with permutaion and combination is

permutation is nPr read as "n pick r", and order does matter.

combination is nCr read as "n choose r", and order does not matter.

See the following online etextbook of probability chapter 3 and 5 for more informations about permutation and combination:

http://faculty.atu.edu/mfinan/actuarieshall/Pbook.pdf

Oct 8, 2018
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Thanks, fiora  !!!

BTW....good to see you  !!!

CPhill  Oct 8, 2018
#7
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If that is true, then instead of having a fucked up lock, we have a fucked up question!

The question says “The lock is opened by pushing down 5 buttons at the same time.”

It doesn’t say “The lock is opened by pushing down 5 buttons in a sequence.”

Buttons that are pressed at the same time do not have a sequence or a permutation. Buttons that are pressed at the same time can only have combinations.

Guest Oct 8, 2018
edited by Guest  Oct 8, 2018
#8
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Mmmmm...I  see what you mean, guest....but....if " at the same time" is true...then my original answer is correct

We don't have to consider any permutations because all we are worried about  is  choosing any 5 numbers at one time from a set of 6

Since  C(6,5)   = 6      and only one of these sets is correct

So    ..  1/6

What do you think???

CPhill  Oct 8, 2018
edited by CPhill  Oct 8, 2018
edited by CPhill  Oct 8, 2018
#9
-1

I think you are correct.

This question describes a true combination lock (a fucked up lock), not a permutation lock.

The question might be fucked up, the lock is definitely fucked up, and your original answer is correct.

Guest Oct 8, 2018
edited by Guest  Oct 8, 2018
edited by Guest  Oct 10, 2018