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A bus driver parks his bus at a bus depot having 20 parking slots duri

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aiming4mba
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A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 03:34
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A bus driver parks his bus at a bus depot having 20 parking slots during lunch break. There are a total of 20 buses parked in the depot including his bus and his bus is not parked at one of the ends. After returning from lunch he finds that there are only 12 buses parked in the lot including his own. If no other bus arrived at the depot during lunch break, then what is the probability that the two buses parked on either side of his bus have left?
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 06:43
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1. the number of buses that left the depot: 20 - 12 = 8
2. the number of combinations to take 8 buses out of 19 (20 - our bus): \(C^{19}_8\)
3. the number of combinations to take 2 buses parked on either side and other 6 buses out of 17 (20 - our bus - 2 buses parked on either side): \(C^{17}_6\)
4. the probability: \(p = \frac{C^{17}_6}{C^{19}_8} = \frac{17!8!*11!}{6!*11!*19!} = \frac{8*7}{19*18} = \frac{28}{171}\)
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 06:59
walker wrote:
1. the number of buses that left the depot: 20 - 12 = 8
2. the number of combinations to take 8 buses out of 19 (20 - our bus): \(C^{19}_8\)
3. the number of combinations to take 2 buses parked on either side and other 6 buses out of 17 (20 - our bus - 2 buses parked on either side): \(C^{17}_6\)
4. the probability: \(p = \frac{C^{17}_6}{C^{19}_8} = \frac{17!8!*11!}{6!*11!*19!} = \frac{8*7}{19*18} = \frac{28}{171}\)



Walker please explain in detail why you divided both the combinations. I could not understand this
It this the only way or is there any other way to solve this problem
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 07:22
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hardnstrong,

A probability can be defined as: the number of desired outcomes/the total number of possible outcomes

In this case, 19C8 is the total number of possible outcomes. We have to choose 8 (because 8 buses have left) out of 19 (because our bus hasn't moved).

Our 'desired' outcome is that the 2 buses next to us have left. Given that this has happened, we have to find the number of ways in which the OTHER buses have left. This is 17C6. 17 because our bus and the 2 buses next to ours are accounted for, and 6 because 2 of the buses that have left were next to us and are accounted for.

Having these values, we divide the second by the first following the probability formula in the first line of this post.
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 07:29
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A number expressing the probability (p) that a specific event will occur, expressed as the ratio of the number of actual occurrences (n) to the number of possible occurrences (N).. By the way, maybe it will be useful for you: math-probability-87244.html

Other way... Hm... I don't see easier way...
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 07:44
walker, what did you get on the GMAT if you dont mind me asking?
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 09:31
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nickk wrote:
walker, what did you get on the GMAT if you dont mind me asking?


750 Q50 V40

It is below my image :)
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   03 Apr 2010, 11:27
Walker, Nickk, thanks for your explanation....understood it now :)
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink] New post   04 Apr 2010, 01:22
walker wrote:
A number expressing the probability (p) that a specific event will occur, expressed as the ratio of the number of actual occurrences (n) to the number of possible occurrences (N).. By the way, maybe it will be useful for you: math-probability-87244.html

Other way... Hm... I don't see easier way...



Thanks walker
Silly me :roll: i got confused here and completely forgot abt total number of outcomes. Seems like spend too much time on maths on weekend (Excess of everything is bad :evil: )

and this link is very useful to understand different approach in probability.
+1 to you mate


nickk thanks to you aswell
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Re: A bus driver parks his bus at a bus depot having 20 parking slots duri [#permalink]
04 Apr 2010, 01:22
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