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A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

104213577705726

lets change the question language to undertand it better... suppose we have 6W, 6B and 6R tiles avaibale..... and we have 2by3 = 6 places to put these tiles.... the question is, in how many ways these tiles can be put, if we cant have only one color pattern..... (means at leat one tiles has to be of different color than rest )

each place can have 3 color to choose from... without any restrctionstotal number of ways = 3^6 = 729

but we cant have all W, all B or all R = 3 desired ways = 729-3 = 726 .. option E

A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different color patterns can the floor be parqueted?

104213577705726

lets change the question language to undertand it better... suppose we have 6W, 6B and 6R tiles avaibale..... and we have 2by3 = 6 places to put these tiles.... the question is, in how many ways these tiles can be put, if we cant have only one color pattern..... (means at leat one tiles has to be of different color than rest )

each place can have 3 color to choose from... without any restrctionstotal number of ways = 3^6 = 729

but we cant have all W, all B or all R = 3 desired ways = 729-3 = 726 .. option E

I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you havea min of 2 options. So total options = 3^5 x 2 = 726.I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.BTW.. did you actually beat that in under 2 mins ?!!!

I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you havea min of 2 options. So total options = 3^5 x 2 = 726.I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.BTW.. did you actually beat that in under 2 mins ?!!!

i did try this approach earlier and found that 3^5 * 2 = 486 ... and its not one of the options ....

frankly, i couldnt do it in under 2 minutes.... took me more than 3 to visualise the logic ... but thats fine for one or two questions i guess... generally i finish maths section with 15 minutes to go .....

I had a logically different but mathematically same approach. Looking for critique..

You have 5 tiles of each color..So for the first slot, you have a min of 3 option - one of the 3 colors. Same for 2nd 3rd 4th and 5th. For the 6th slot, you havea min of 2 options. So total options = 3^5 x 2 = 726.I have a feeling that this reasoning is flawed, but am unable to point it. Please let me know if you think that it is erroneous.BTW.. did you actually beat that in under 2 mins ?!!!

i did try this approach earlier and found that 3^5 * 2 = 486 ... and its not one of the options ....

frankly, i couldnt do it in under 2 minutes.... took me more than 3 to visualise the logic ... but thats fine for one or two questions i guess... generally i finish maths section with 15 minutes to go .....