document.write( "Question 1074717: Let A={1,2,3,4,5}.
\n" ); document.write( "(a) How many total functions f∶ A→A are there?
\n" ); document.write( "(b) How many of the functions in (a) are one-to-one? \r
\n" ); document.write( "\n" ); document.write( "Can someone please explain on how to start and solve these type of question? Thank you! \n" ); document.write( "

Algebra.Com's Answer #689379 by ikleyn(52800) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Let A={1,2,3,4,5}.
\n" ); document.write( "(a) How many total functions f∶ A→A are there?
\n" ); document.write( "(b) How many of the functions in (a) are one-to-one? \r
\n" ); document.write( "\n" ); document.write( "Can someone please explain on how to start and solve these type of question? Thank you!
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document.write( "The short explanation is this:\r\n" );
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document.write( "(a)  Every function f: A --> A correlates some values of the set A to each element of the set A.\r\n" );
document.write( "     Every function f: A --> A is such a correlation.\r\n" );
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document.write( "     Function f can correlate ANY of 5 values 1, 2, 3, 4 and/or 5 to the element \"1\" : FIVE options.\r\n" );
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document.write( "     Function f can correlate ANY of 5 values 1, 2, 3, 4 and/or 5 to the element \"2\" : FIVE options.\r\n" );
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document.write( ". . . and so on till 5.\r\n" );
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document.write( "   In all, there are  different functions.\r\n" );
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document.write( "(b)  One-to-one function in this context is simply a permutation (\"without repetition\").\r\n" );
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document.write( "    The number of permutations of 5 objects is 5! = 120 - very well known fact.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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