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If 7 distinct car accidents happened during 7 days, what is

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If 7 distinct car accidents happened during 7 days, what is [#permalink] New post 07 Jun 2010, 02:34
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If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?

Official solution:

[Reveal] Spoiler:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)


I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.

Thanks.
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Re: Probability car accidents [#permalink] New post 07 Jun 2010, 03:09
In general, the number of ways that "m" objects can be distributed into "n" boxes is n^m (When the objects and boxes are distinguishable, and a box can be empty) I've attached a little reference chart for you to remember the formula for these kind of problems. For the GMAT I wouldn't bother deriving them - just remember them.

So distributing the 7 boxes into the 7 days needs 7^7 ways.

It must be clear to you that if all 7 happened on the same day, it could happen in 7 ways, (since it depends on which day this happened)

Prob = 7 / 7^7 = 1 / 7^6
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File comment: Here's a nice little chart for these kind of repetition problems.
Combinatorics.jpg
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Re: Probability car accidents [#permalink] New post 07 Jun 2010, 05:05
Thanks for your reply. I figured it out. Very simple.
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Re: Probability car accidents [#permalink] New post 01 Aug 2013, 08:22
As I a remember there is one formula for distribution of n objects to r people, that formula consider all cases of distribution of the objects in chunk of 0 , 1 , 2 .. so on.

Formula = (n+r-1)C(r-1) (bcz i think accidents can happen or not happen on any particular day or even multiple accidents can happen) thus this formula qualifies to find all such cases.

13C6 = 1716

desirable cases are 7.

thus Prob = 7/1716

I hope i am right.
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Re: If 7 distinct car accidents happened during 7 days, what is [#permalink] New post 10 Dec 2013, 07:24
nonameee wrote:
If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?

Official solution:

[Reveal] Spoiler:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)


I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.

Thanks.


7C6/7^7=1/7^6

Pretty straightforward
Cheers
J :)
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Re: If 7 distinct car accidents happened during 7 days, what is [#permalink] New post 31 Jan 2014, 12:41
jlgdr wrote:
nonameee wrote:
If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?

Official solution:

[Reveal] Spoiler:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)


I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.

Thanks.


7C6/7^7=1/7^6

Pretty straightforward
Cheers
J :)


Hi jlgdr,

Can you please explain why 7C6 in numerator.

Thanks
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Re: If 7 distinct car accidents happened during 7 days, what is [#permalink] New post 31 Jan 2014, 13:03
vivekisthere wrote:
jlgdr wrote:
nonameee wrote:
If 7 distinct car accidents happened during 7 days, what is the probability that all the accidents happened on a particular day?

Official solution:

[Reveal] Spoiler:
OMEGA = 7^7
A = 7
P(A) A/OMEGA = 1/(7^6)


I don't understand the formula for counting the sample space. Your inputs/explanation would be very appreciated.

Thanks.


7C6/7^7=1/7^6

Pretty straightforward
Cheers
J :)


Hi jlgdr,

Can you please explain why 7C6 in numerator.

Thanks



Sure. Each accident can happen in each of the 7 days.
We want the scenario in which all happen in the same day
Therefore, since all accidents will happen in the same day then we only need to pick in which day out of the 7 days will all the accidents happen

So 7C1 = 7C6 = 7

Hope its clear
J
Re: If 7 distinct car accidents happened during 7 days, what is   [#permalink] 31 Jan 2014, 13:03
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