Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Oct 2009
Posts: 211

A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
15 Nov 2009, 05:38
2
This post received KUDOS
8
This post was BOOKMARKED
Question Stats:
50% (02:59) correct
50% (01:53) wrong based on 255 sessions
HideShow timer Statistics
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. \((\frac{1}{3})^6*(\frac{1}{2})^3\) B. \((\frac{1}{3})^6*(\frac{1}{2})\) C. \((\frac{1}{3})^4\) D. \((\frac{1}{3})^2*(\frac{1}{2})\) E. \(5*(\frac{1}{3})^2\) Happy solving!
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html
Last edited by Bunuel on 11 Feb 2012, 03:26, edited 1 time in total.
Edited the question and added the OA



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Snappy dresser.. :P [#permalink]
Show Tags
15 Nov 2009, 06:20
17
This post received KUDOS
Expert's post
5
This post was BOOKMARKED
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?
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, \(p=\frac{1}{2}*\frac{1}{3}*\frac{1}{3}=\frac{1}{18}\); \(P=1*\frac{2}{9}*\frac{1}{18}=\frac{1}{81}=\frac{1}{3^4}\) Answer: C (\(\frac{1}{3^4}\)).
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 29 Oct 2009
Posts: 211

Re: Snappy dresser.. :P [#permalink]
Show Tags
15 Nov 2009, 06:55
2
This post received KUDOS
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/compilationoftipsandtrickstodealwithremainders86714.html#p651942
Word Problems Made Easy! 1) Translating the English to Math : http://gmatclub.com/forum/wordproblemsmadeeasy87346.html 2) 'Work' Problems Made Easy : http://gmatclub.com/forum/workwordproblemsmadeeasy87357.html 3) 'Distance/Speed/Time' Word Problems Made Easy : http://gmatclub.com/forum/distancespeedtimewordproblemsmadeeasy87481.html



Manager
Joined: 13 Aug 2009
Posts: 201

Re: Snappy dresser.. :P [#permalink]
Show Tags
15 Nov 2009, 09:11
2
This post received KUDOS
Good problem.
The first day the man can wear anything: (Shoes)*(Shirts)*(Pants) (2/2)*(3/3)*(3/3)
The second day the man must wear the same pair of shoes and not wear the shirt and pants from the day before: (1/2)*(2/3)*(2/3)
The final day, the man must continue to wear the same pair of shoes and wear the one shirt and one pants that were not worn: (1/2)*(1/3)*(1/3)
So multiplay all together to get the probability of this happening each consecutive day:
(2/2)*(3/3)*(3/3)*(1/2)*(2/3)*(2/3)*(1/2)*(1/3)*(1/3)= (1/3)^4
ANSWER: C.



Manager
Joined: 03 Apr 2013
Posts: 179

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
13 Nov 2013, 12:27
1
This post received KUDOS
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!
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 29 Sep 2015
Posts: 2

A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
05 Oct 2015, 08:59
1
This post received KUDOS
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



Manager
Joined: 24 Jul 2009
Posts: 73
Location: United States

Re: Snappy dresser.. :P [#permalink]
Show Tags
15 Nov 2009, 11:37
h2polo,
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.



Manager
Joined: 13 Aug 2009
Posts: 201

Re: Snappy dresser.. :P [#permalink]
Show Tags
16 Nov 2009, 03:51
Oh no... there is no competing with Bunuel. He solves the unsolvable. Hahaha...



Senior Manager
Joined: 01 Mar 2009
Posts: 367
Location: PDX

Re: Snappy dresser.. :P [#permalink]
Show Tags
18 Nov 2009, 16:53
I missed out on the activities in this forum lately and it's again a joy to read Bunuel's answers. Kudos
_________________
In the land of the night, the chariot of the sun is drawn by the grateful dead



Intern
Joined: 01 Nov 2009
Posts: 16

Re: probability of wearing dress [#permalink]
Show Tags
05 Apr 2010, 05:02
My question is:
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..



Manager
Joined: 10 Aug 2009
Posts: 123

Re: probability of wearing dress [#permalink]
Show Tags
05 Apr 2010, 08:44
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.



Intern
Joined: 01 Nov 2009
Posts: 16

Re: probability of wearing dress [#permalink]
Show Tags
16 Apr 2010, 01:15
Aah!! i think I got confused between number of ways and probability. probability of choosing same shoe= 1C1/2C1 Many thanks



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
26 Aug 2013, 02:53



Manager
Joined: 04 Sep 2012
Posts: 100
Location: Philippines
Concentration: Marketing, Entrepreneurship
Schools: Ross (Michigan)  Class of 2017
GMAT 1: 620 Q48 V27 GMAT 2: 660 Q47 V34 GMAT 3: 700 Q47 V38
GPA: 3.25
WE: Sales (Manufacturing)

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
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?
A. \((\frac{1}{3})^6*(\frac{1}{2})^3\)
B. \((\frac{1}{3})^6*(\frac{1}{2})\)
C. \((\frac{1}{3})^4\)
D. \((\frac{1}{3})^2*(\frac{1}{2})\)
E. \(5*(\frac{1}{3})^2\)
Happy solving! 1st Day  \(\frac{3}{3}\) shirts \(*\) \(\frac{2}{2}\) shoes \(*\) \(\frac{3}{3}\) pants 2nd Day  \(\frac{2}{3}\) shirts, \(*\) \(\frac{1}{2}\) shoes \(*\) \(\frac{2}{3}\) pants 3rd Day  \(\frac{1}{3}\) shirts, \(*\) \(\frac{1}{2}\) shoes \(*\) \(\frac{1}{3}\) pants Answer is \((\frac{1}{3})^4\)



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16027

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16027

Re: A man chooses an outfit from 3 different shirts, 2 different [#permalink]
Show Tags
11 Nov 2016, 16:51
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). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A man chooses an outfit from 3 different shirts, 2 different
[#permalink]
11 Nov 2016, 16:51







