Rectangular Floor: A challenge Q

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hardikm: Senior | Next Rank: 100 Posts; Posts: 64; Joined: Mon Apr 27, 2009 2:52 pmFollowed by: 1 member; Location: Dallas; Thanked: 10 times

by hardikm » Tue May 31, 2011 10:15 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.
1. 104
2. 213
3. 577
4. 705
5. 726

Source: GMAT Club App

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Source: Beat The GMAT — Data Sufficiency | Tue May 31, 2011 10:15 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue May 31, 2011 10:27 am

Hi,
there are 6 blocks on the floor. Each block can have either of the three colors. So, number of patterns is 3^6 but this includes patterns which are all 6 white, all 6 black and all 6 red. But, there are only 5 blocks of each color. so, we need to subtract these '3'.
So, number of patterns is 3^6-3 = 726.
Hence, 5
Pleas post such questions in 'Problem Solving' section.

Cheers!

Last edited by Frankenstein on Tue May 31, 2011 10:30 am, edited 1 time in total.

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue May 31, 2011 10:29 am

IMO E

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