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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pm; Thanked: 15 times; Followed by:1 members; GMAT Score:690

Floor

by crackgmat007 » Tue Oct 20, 2009 7:03 am

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?

104
213
577
705
726

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Source: Beat The GMAT — Problem Solving | Tue Oct 20, 2009 7:03 am

mp2437: Master | Next Rank: 500 Posts; Posts: 177; Joined: Thu Aug 14, 2008 11:59 am; Thanked: 25 times

by mp2437 » Tue Oct 20, 2009 8:25 am

Choice E. You have to fill up 6 blocks, and each block could be either white, black, or red, a total of 3 picks.

So, 6 blocks could have a total of 3^6, or 729
different combinations. Since we only have 5 blocks of each color, you have to rule out the combinations of all 6 being white, black or red, so 729 - 3 = 726.

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pm; Thanked: 15 times; Followed by:1 members; GMAT Score:690

by crackgmat007 » Tue Oct 20, 2009 4:21 pm

So, 6 blocks could have a total of 3^6, or 729

Can you explain 3^6 pls?

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ssuarezo: Master | Next Rank: 500 Posts; Posts: 126; Joined: Wed Jun 24, 2009 1:12 pm; Location: Montreal; Thanked: 2 times; GMAT Score:510

by ssuarezo » Tue Oct 20, 2009 9:02 pm

crackgmat007 wrote:
So, 6 blocks could have a total of 3^6, or 729
Can you explain 3^6 pls?

You need 6 positions, and each one can be 3 colors, so, pos1=3 posibilities, same for pos2, pos3, ... pos6. At the end u have 3x3x3x3x3x3 arrangements, that it, 3^6
What is the OA?

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crackgmat007: Legendary Member; Posts: 882; Joined: Fri Feb 20, 2009 2:57 pm; Thanked: 15 times; Followed by:1 members; GMAT Score:690