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Probability question w/ exponents

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undvaulter
 Post subject: Probability question w/ exponents
 Post Posted: Mon Apr 12, 2010 9:09 am 
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Posts: 6
A man chooses an outfit from 3 different shirts, 2 different pairs of shoes, and 3 different pants. If he randomly selects 1 shirt, 1 pair of shoes, and 1 pair of pants each morning for 3 days, what is the probability that he wears the same pair of shoes each day, but that no other piece of clothing is repeated?


A (1/3)^6 x (1/2)^3

B (1/3)^6 x (1/2)

C (1/3)^4

D (1/3)^2 x (1/2)

E 5(1/3)^2
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ps63739
 Post subject: Re: Probability question w/ exponents
 Post Posted: Mon Apr 12, 2010 9:08 pm 
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Students


Posts: 54
Let's take day by day -

Day 1 (favourable outcome) - He can select shoes two ways, Shirts and Pants each 3 ways = 2*3*3.
Total number of outcomes = 2*3*3
So P(Day1) = 2*3*3/2*3*3 = 1
Day 2 (Favourable outcomes) - He can select shoes 1 (he has to wear the same shoe) way and select the pants and shirts 2 ways each (as he cannot wear the Shirt and Pant he wore Day1) = 1*2*2
Total outcomes = 2*3*3

So P(Day2) = 1*2*2/2*3*3 = 2/9.
Day 3 - in the similar fashion
P(day3) = 1/18

Now probability here will be multiplied.

Total probability will be = P(Day1) happens and P(Day2) happens and P(Day3) happnes.

That gives P= 1*(2/9)*(1/18)
= 1/3^4.
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Ben Ku
 Post subject: Re: Probability question w/ exponents
 Post Posted: Tue Apr 13, 2010 1:08 am 
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ManhattanGMAT Staff


Posts: 824
Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.

_________________
Ben Ku
Instructor
ManhattanGMAT
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shalinibhatia15
 Post subject: Re: Probability question w/ exponents
 Post Posted: Mon May 17, 2010 11:28 pm 
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Students


Posts: 13
hi this is from gmatprep

Ben Ku wrote:
Please cite the source (author) of this problem. We cannot reply unless a source is cited (and, if no source is cited, we will have to delete the post!). Thanks.
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mschwrtz
 Post subject: Re: Probability question w/ exponents
 Post Posted: Thu Oct 28, 2010 5:42 pm 
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ManhattanGMAT Staff


Posts: 506
Thanks, we'll move it over to that forum.
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