document.write( "Question 1202852: In a certain city, there are seven streets going north-south and five streets going east-west. How many street paths start at the southwest corner of the city, end at the northeast corner of the city, and have the shortest possible length?
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Algebra.Com's Answer #838017 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "In a certain city, there are seven streets going north-south and five streets going east-west.
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document.write( "Each such path is a combination of elementary 7 south->north parts/blocs and \r\n" );
document.write( "5 west->east parts/blocks, 7+5 = 12 blocks, in total.\r\n" );
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document.write( "So, using designation/letter V for south->north blocks (\"vertical\") and designation/letter H (\"horizontal\") \r\n" );
document.write( "for west->east blocks, each path can be coded as a word of 12 letters \"V\" and \"H\".\r\n" );
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document.write( "There is one-to-one correspondence between such paths and such words.\r\n" );
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document.write( "So, we can say that the number of paths equals the number of words of the length 12,\r\n" );
document.write( "written using letter V and H.  Repeating of letters is allowed.\r\n" );
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document.write( "From Combinatorics, it is known that the number of such words is  \r\n" );
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document.write( "    \"12%21%2F%287%21%2A5%21%29\" = after reduction of the fraction = \"%2812%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%29\" = \"C%5B12%5D%5E5\" = \"C%5B12%5D%5E7\" = 792.\r\n" );
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document.write( "Indeed, from the total 12 positions of the word, 7 positions for letters \"V\" can be selected \r\n" );
document.write( "in  \"C%5B12%5D%5E7\"  different ways; the rest 5 positions are occupied by the letters \"H\".\r\n" );
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document.write( "It gives us the answer to the problem's question: there are 792 such paths.\r\n" );
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document.write( "    How many distinguishable ways are there to place in line 7 red and 5 white balls, if they distinct only by color ?\"\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar  (and different)  solved problems,  look into the lesson\r
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