document.write( "Question 837998: Hello, My name is Sheila, and I would really like your help in solving this problem, and how to set it up.
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document.write( "The problem is a follow: How many one-to-one correspondence are there between the sets { x,y,z,u,v ] and {1,2,3,4,5 } if in each correspondence:
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document.write( "A. x must correspond to 5
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document.write( "B. x must correspond to 5 and y to 1
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document.write( "C. x,y,z must correspond to odd numbers \n" );
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Algebra.Com's Answer #506159 by Edwin McCravy(20059)![]() ![]() You can put this solution on YOUR website! \r\n" ); document.write( " { x,y,z,u,v ] and {1,2,3,4,5 }\r\n" ); document.write( "--------------------------------------------\r\n" ); document.write( "A. x must correspond to 5\r\n" ); document.write( "\r\n" ); document.write( "{(x,5),(y,_),(z,_),(u,_),(v,_)}\r\n" ); document.write( "\r\n" ); document.write( "We can choose \r\n" ); document.write( "y's 2nd coordinate 4 ways,\r\n" ); document.write( "z's 2nd coordinate 3 ways,\r\n" ); document.write( "u's 2nd coordinate 2 ways,\r\n" ); document.write( "v's 2nd coordinate 1 way.\r\n" ); document.write( "\r\n" ); document.write( "Answer: 4·3·2·1 = 4! = 24 ways\r\n" ); document.write( "--------------------------------------------\r\n" ); document.write( "B. x must correspond to 5 and y to 1\r\n" ); document.write( "\r\n" ); document.write( "{(x,5),(y,1),(z,_),(u,_),(v,_)}\r\n" ); document.write( "\r\n" ); document.write( "We can choose\r\n" ); document.write( "z's 2nd coordinate 3 ways,\r\n" ); document.write( "u's 2nd coordinate 2 ways,\r\n" ); document.write( "v's 2nd coordinate 1 way.\r\n" ); document.write( "\r\n" ); document.write( "Answer: 3·2·1 = 3! = 6 ways\r\n" ); document.write( "--------------------------------------------\r\n" ); document.write( "C. x,y,z must correspond to odd numbers\r\n" ); document.write( "\r\n" ); document.write( "{(x,_),(y,_),(z,_),(u,_),(v,_)}\r\n" ); document.write( "\r\n" ); document.write( "We can choose \r\n" ); document.write( "x's 2nd coordinate 3 ways, (1, 3 or 5)\r\n" ); document.write( "y's 2nd coordinate 2 ways,\r\n" ); document.write( "z's 2nd coordinate 1 way.\r\n" ); document.write( "u's 2nd coordinate 2 ways, (2 or 4)\r\n" ); document.write( "v's 2nd coordinate 1 way.\r\n" ); document.write( "\r\n" ); document.write( "Answer: 3·2·1·2·1 = 3!2! = 6·2 = 12 ways\r\n" ); document.write( "\r\n" ); document.write( "Edwin\n" ); document.write( " |