A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?
A. 104
B. 213
C. 577
D. 705
E. 726
perhaps I got the solution but went crazy while doing it using combinatrics
Solution:
3^6, or 729
you have to rule out the combinations of all 6 being white, black or red, so 729 - 3 = 726.
----
5c5*5c1*3c2 + 5c4*5c1*5c1*3c2 + 5c3*5c2*5c1*3! + 5c2*5c2*5c2 , even the last one fragment comes out to be 1000 which is far more then right ans
P&C
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 468
- Joined: Mon Jul 25, 2011 10:20 pm
- Thanked: 29 times
- Followed by:4 members
GMAT/MBA Expert
- lunarpower
- GMAT Instructor
- Posts: 3380
- Joined: Mon Mar 03, 2008 1:20 am
- Thanked: 2256 times
- Followed by:1535 members
- GMAT Score:800
For pretty much all combinatorics problems:
* If there are only a small number of possibilities, just make lists, and count stuff.
(e.g., OG quant supplement #132)
* If there are too many things to list and count.. is it relatively straightforward to calculate the number of possibilities directly?
- If so, do it.
- If not, think about the probability of the opposite event.
In this case, it would be absolutely horrible to calculate the probability directly. The opposite event, though, is "everything in the world except all red, all white, or all black". That's not so bad.
* If there are only a small number of possibilities, just make lists, and count stuff.
(e.g., OG quant supplement #132)
* If there are too many things to list and count.. is it relatively straightforward to calculate the number of possibilities directly?
- If so, do it.
- If not, think about the probability of the opposite event.
In this case, it would be absolutely horrible to calculate the probability directly. The opposite event, though, is "everything in the world except all red, all white, or all black". That's not so bad.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Floor area = b*h = 2*3 = 6 sq. meters.vipulgoyal wrote:A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?
A. 104
B. 213
C. 577
D. 705
E. 726
Area of each block = b*h = 1*1 = 1 sq. meters.
Total number of blocks required = Floor area/Block area = 6/1 = 6 blocks.
Good combinations = Total possible combinations - Bad combinations
Total possible combinations:
For each block, there 3 options: white, black, or red.
Since there are 3 options for each of the 6 blocks, we get:
3*3*3*3*3*3 = 729.
Bad combinations:
Since there are ONLY 5 of each color, all 6 blocks CANNOT be of the same color.
Thus, there are 3 bad combinations:
All white, all black, all red.
Good combinations = Total - Bad = 729-3 = 726.
The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
There are six spots on the 2x3 floor. We'll label them as #1, 2, 3, 4, 5, and 6.vipulgoyal wrote:A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. If each block measures 1 by 1 meter, in how many different color patterns can the floor be parqueted?
A. 104
B. 213
C. 577
D. 705
E. 726
Take the task of placing a block in each spot and break it into stages.
Stage 1: Select a colored block for space #1
There are 3 colors to choose from, so we can complete stage 1 in 3 ways
Stage 2: Select a colored block for space #2
There are 3 colors to choose from, so we can complete stage 2 in 3 ways
Stage 3: Select a colored block for space #3
There are 3 colors to choose from, so we can complete stage 3 in 3 ways
.
.
.
Stage 6: Select a colored block for space #6
There are 3 colors to choose from, so we can complete stage 6 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus place 6 blocks) in (3)(3)(3)(3)(3)(3) ways (= 729 ways)
Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775
IMPORTANT: This method allows for the possibility that all 6 blocks being the same color. However, since there are only 5 blocks of each color, we can't have all 6 blocks the same color.
So, we need to subtract from 729 all of the arrangements where the 6 blocks are the same color.
Well, there are 3 such arrangements: 1) all blocks white, 2) all blocks black, and 3) all blocks red.
When we subtract the 3 impossible arrangements from 729, we get 726
Answer: E
Cheers,
Brent