document.write( "Question 1207461: Please resolve this question. You have two 10 cents coins, two $1 coins, one fifty cents coin and a $2 coin. one coin is randomly chosen and is not replaced. two more coins are then randomly chosen, What is the total number of possible outcomes for this chance experiment. \n" ); document.write( "

Algebra.Com's Answer #845348 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Please resolve this question. You have two 10 cents coins, two $1 coins, one fifty cents coin and a $2 coin.
\n" ); document.write( "one coin is randomly chosen and is not replaced. two more coins are then randomly chosen,
\n" ); document.write( "What is the total number of possible outcomes for this chance experiment.
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\n" ); document.write( "\n" ); document.write( "        The solution by Edwin is incorrect.
\n" ); document.write( "        It is incorrect, since Edwin counts many identical outcomes as different outcomes.\r
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\n" ); document.write( "\n" ); document.write( "        I apply totally different logic and obtain totally different solution and answer.\r
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document.write( "The problem's question is the same (= is equivalent) as to ask \r\n" );
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document.write( "    having two 10-cent coins, two 1-dollar coins, one 50-cent coin and one 2-dollar coin,\r\n" );
document.write( "    in how many different ways can you choose a triple of coins (without looking on the order).\r\n" );
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document.write( "Had all 6 coins be different, we would choose  =  =  = 5*4 = 20 \r\n" );
document.write( "different triples.\r\n" );
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document.write( "But some triples are indistinguishable, because they have indistinguishable coins;\r\n" );
document.write( "therefore, we should count indistinguishable triples only ONCE, NOT twice.\r\n" );
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document.write( "So, you have  the set  AABBCD  to start choosing triples from it.\r\n" );
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document.write( "All unique distinct triples are\r\n" );
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document.write( "    ABC    (no repetition)\r\n" );
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document.write( "    ABD    (no repetition)\r\n" );
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document.write( "    ACD    (no repetition)\r\n" );
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document.write( "    BCD    (no repetition)\r\n" );
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document.write( "    AAB    (with repeating A)\r\n" );
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document.write( "    AAC    (with repeating A)\r\n" );
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document.write( "    AAD    (with repeating A)\r\n" );
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document.write( "    ABB    (with repeating B)\r\n" );
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document.write( "    BBC    (with repeating B)\r\n" );
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document.write( "    BBD    (with repeating B)\r\n" );
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document.write( "Thus these 10 outcomes are all possible different outcomes in this experiment.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Hope Edwin will agree with this solution,
\n" ); document.write( "and we will celebrate the triumph of reason together.\r
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