document.write( "Question 1196436: how many one-to-one correspondences are there between two sets with k elements each? \n" ); document.write( "

Algebra.Com's Answer #829258 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "ANSWER.  k! = 1*2*3* . . . *(k-1)*k.\r\n" );
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document.write( "Explanation.\r\n" );
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document.write( "Let the sets be A and B: they have equal numbers of elements.\r\n" );
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document.write( "1st element of A can be related to any of k elements of B.\r\n" );
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document.write( "2nd element of A can be related to any of remaining (k-1) elements of B.\r\n" );
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document.write( "3rd element of A can be related to any of remaining (k-2) elements of B.\r\n" );
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document.write( "   . . . and so on . . . \r\n" );
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document.write( "It gives the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The problem is the same as to ask \r
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document.write( "        \" how many are there permutations of a set of k elements ? \"\r\n" );
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