document.write( "Question 601074: How many ways can you rearrange 12 eggs ? Do you use 12! Or permutations ? \n" ); document.write( "

Algebra.Com's Answer #379588 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!
There are 12 places to pick a place for the 1st egg,
\n" ); document.write( "For each of those 12 places, there remain 11 places to put the 2nd egg.
\n" ); document.write( "That 12ｷ11 ways to place the first two 3ggs.
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document.write( "Factoriala ARE permutations.\r\n" );
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document.write( "The best way is to think it out:\r\n" );
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document.write( "There are 12 ways to place egg #1 in the carton.\r\n" );
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document.write( "For each of those 12 ways to place the 1st egg, there\r\n" );
document.write( "remain 11 places in the carton to place egg #2.\r\n" );
document.write( "That's 12ｷ11 ways to place the first 2 eggs in the\r\n" );
document.write( "carton.\r\n" );
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document.write( "For each of those 12ｷ11 ways to place the 1st 2 eggs,\r\n" );
document.write( "there remain 10 places in the carton to place egg #3.\r\n" );
document.write( "That's 12ｷ11ｷ10 ways to place the first 3 eggs in the\r\n" );
document.write( "carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10 ways to place the 1st 3 eggs,\r\n" );
document.write( "there remain 9 places in the carton to place egg #4.\r\n" );
document.write( "That's 12ｷ11ｷ10ｷ9 ways to place the first 4 eggs in the\r\n" );
document.write( "carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9 ways to place the 1st 4\r\n" );
document.write( "eggs, there remain 8 places in the carton to place egg\r\n" );
document.write( "#5. That's 12ｷ11ｷ10ｷ9ｷ8 ways to place the first 5 eggs in\r\n" );
document.write( "the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8 ways to place the 1st 5\r\n" );
document.write( "eggs, there remain 7 places in the carton to place egg\r\n" );
document.write( "#6. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the first 6 eggs\r\n" );
document.write( "in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7 ways to place the 1st 6\r\n" );
document.write( "eggs, there remain 6 places in the carton to place egg\r\n" );
document.write( "#7. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the first 7\r\n" );
document.write( "eggs in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6 ways to place the 1st\r\n" );
document.write( "7 eggs, there remain 5 places in the carton to place egg\r\n" );
document.write( "#8. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the first 8\r\n" );
document.write( "eggs in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5 ways to place the\r\n" );
document.write( "1st 8 eggs, there remain 4 places in the carton to place\r\n" );
document.write( "egg #9. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the\r\n" );
document.write( "first 9 eggs in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4 ways to place the\r\n" );
document.write( "1st 9 eggs, there remain 3 places in the carton to place\r\n" );
document.write( "egg #10. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place the\r\n" );
document.write( "first 10 eggs in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3 ways to place\r\n" );
document.write( "the 1st 10 eggs, there remain 2 places in the carton to\r\n" );
document.write( "place egg #11. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to\r\n" );
document.write( "place the first 11 eggs in the carton.\r\n" );
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document.write( "For each of those 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2 ways to place\r\n" );
document.write( "the 1st 11 eggs, there remain only 1 place in the carton\r\n" );
document.write( "to place egg #12. That's 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 ways\r\n" );
document.write( "to place all 12 eggs in the carton.\r\n" );
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document.write( "Answer: 12ｷ11ｷ10ｷ9ｷ8ｷ7ｷ6ｷ5ｷ4ｷ3ｷ2ｷ1 = 12!\r\n" );
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document.write( "That's also the number of permutations of 12 things taken all 12\r\n" );
document.write( "at a time.    \r\n" );
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document.write( "nPn or P(n,n) = n!\r\n" );
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document.write( "Edwin

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