document.write( "Question 885505: A company has 12 construction workers. The manager plans to assign 3 to job site A, 4 to job site B and 5 to job site C. In how many different ways can the manager make this assignment? \n" ); document.write( "
Algebra.Com's Answer #535211 by Edwin McCravy(20055)\"\" \"About 
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document.write( "Since choosing Tom, Dick, and Harry is the same as choosing Dick, Harry, and\r\n" );
document.write( "Tom, order doesn't matter, so we use combinations, not permutations.\r\n" );
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document.write( "Choose the workers for job site A as any 3 of the 12 in C(12,3)=220 ways.\r\n" );
document.write( "Choose the workers for job site B as any 4 of the remaining 9 in C(9,4)=126 ways.\r\n" );
document.write( "Choose the workers for job site C as the remaining 5 in C(5,5)=1 way. \r\n" );
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document.write( "Answer: 220×126×1 = 27720 ways\r\n" );
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document.write( "Notice that it does not matter in which order we choose the workers for the\r\n" );
document.write( "three sites. For instance suppose we chose workers for C first, then A, then B:\r\n" );
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document.write( "Choose the workers for job site C as any 5 of the 12 in C(12,5)=792 ways.\r\n" );
document.write( "Choose the workers for job site A as any 3 of the remaining 7 in C(7,3)=35 ways.\r\n" );
document.write( "Choose the workers for job site B as the remaining 4 in C(4,4)=1 way. \r\n" );
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document.write( "Answer: 792×35×1 = 27720 ways\r\n" );
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document.write( "Although we multiplied different numbers together, we get the same\r\n" );
document.write( "answer 27720 both times.  You can try other picking orders and you'll \r\n" );
document.write( "see you will always get 27720 in the end.\r\n" );
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document.write( "Edwin
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