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A man chooses an outfit from 3 different shirts, 2 different [#permalink]

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15 Nov 2009, 05:38

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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?

Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Last edited by Bunuel on 11 Feb 2012, 03:26, edited 1 time in total.

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?

1) \((1/3)^6*(1/2)^3\)

2) \((1/3)^6*(1/2)\)

3) \((1/3)^4\)

4) \((1/3)^2*(1/2)\)

5) \(5*(1/3)^2\)

Happy solving!

For the first day he can choose any outfit, \(p=1\);

For the second day he must choose the same shoes as on the first day and different shirts and pants form the first day's, \(p=\frac{1}{2}*\frac{2}{3}*\frac{2}{3}=\frac{2}{9}\);

For the third day he must choose the same shoes as on the first day and different shirts and pants from the first and second day's, \(p=\frac{1}{2}*\frac{1}{3}*\frac{1}{3}=\frac{1}{18}\);

Having Bunuel post is as good as posting the OA...

In fact, better.. because not only are the answers always right but the explanations always perfect!

+1 to you Bunuel! (I think soon you'll have more kudos than posts!)

Cheers! _________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942

Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/word-problems-made-easy-87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/work-word-problems-made-easy-87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distance-speed-time-word-problems-made-easy-87481.html

Kudos to you as well, u have been ruling the quant section, soon i see u becoming the moderator. But keep in mind, u r competing with the best....Bunuel.

day 2: probability of choosing shoe should be 1 as we can not choose one of the two shoes rather the one that was already chosen on day 1 same for day 3 please explain..

san03: On day 2 (and 3), the probability for the shoes should be 1/2 This is because given a shoe was chosen on day 1, the probability of choosing that same shoe the next day is 1/2.

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]

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13 Nov 2013, 12:27

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Another way to look at the problem :- !. Since a single pair of shoes has to be chosen and worn for all the three days, No. of ways of selecting one pair of shoes from the available two = 2C1 = 2. 2. Now the remaining task for us is to choose different shirts and pants for the three days : - 1st day = 3 X 3 2nd day = 2 X 2 3rd day = 1 X 1 Multiplying all the terms 2C1 X 2 X 2 X 3 X 3 X 1 X 1 (Numerator)

now what will come in the denominator? day Pants Pair of shoes Shirts 1st 3 2 3 2nd 3 2 3 3rd 3 2 3

That is = 3^3 X 2^3 X 3^3 (Denominator)

When the Numerator is divided by the Denominator, you will get the required answer = 1/(3)^4. Kudos for the answer! _________________

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]

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23 Jul 2014, 05:47

sriharimurthy wrote:

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?

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]

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04 Oct 2015, 06:22

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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A man chooses an outfit from 3 different shirts, 2 different [#permalink]

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05 Oct 2015, 08:59

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the probability of choosing a unique set of attire on the fisrt day = 1. from the second day, if I choose to wear the same pair of shoes(s1) on second and third day, then the probaility = [(1/2)*(2/3)*(2/3)]*[(1/2)*(1/3)*(1/3)]= 1/81.

Similarly,I can choose to wear shoes(S2) on all three days. Here as well the probability = 1/81.

Hence, the total probaility = 1/81 + 1/81= 2/81

gmatclubot

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