document.write( "Question 534682: Consider a large bag of coins, consisting of only quarters ($0.25), dimes ($0.10), and nickels ($0.05). 40% of the coins are nickels, 35% are dimes, and 25% are quarters.\r
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Algebra.Com's Answer #351642 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Consider a large bag of coins, consisting of only quarters ($0.25), dimes ($0.10), and nickels ($0.05). 40% of the coins are nickels, 35% are dimes, and 25% are quarters.
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document.write( "You must draw either 5 quarters of 4 quarters and a nickel or dime.\r\n" );
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document.write( "Suppose there are 100N coins consisting of 40N nickels, 35N dimes, and 25N\r\n" );
document.write( "quarters.  Note: there are 75N non-quarters\r\n" );
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document.write( "The number of successes equals\r\n" );
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document.write( "the number of ways to draw 5 quarters is C(25N,5)\r\n" );
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document.write( "plus\r\n" );
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document.write( "the number of ways to draw 4 quarters and 1 non-quarter is C(25N,4)·(75N)\r\n" );
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document.write( "So the number of successes is\r\n" );
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document.write( "C(25N,5) + C(25N,4)·(75N)\r\n" );
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document.write( "\"%28++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2825N-4%29%29%2F5%21\" + \"expr%28%28%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%29%2F4%21%29%2A75N\"  \r\n" );
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document.write( "Put the (75N) in the numerator of the second fraction\r\n" );
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document.write( "\"%28++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2825N-4%29%29%2F5%21\" + \"expr%28%28%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2875N%29%29%2F4%21%29\" \r\n" );
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document.write( "We get a least common denominator of 5! by multiplying the second fraction\r\n" );
document.write( "by \"5%2F5\"\r\n" );
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document.write( "\"%28++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2825N-4%29%29%2F5%21\" + \"expr%28%28%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2875N%295%29%2F%284%215%29%29\" \r\n" );
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document.write( "\"%28++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2825N-4%29%29%2F5%21\" + \"expr%28%28%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%28375N%29%29%2F5%21%29\"\r\n" );
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document.write( "Factor the numerator:\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%28%2825N-4%29+%2B+%28375N%29%29%2F5%21\"\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%2825N-4+%2B+375N%29%2F5%21\"\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%28400N-4%29%2F5%21\"\r\n" );
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document.write( "The number of possible ways is the number of ways to select any \r\n" );
document.write( "5 coins from the 100N coins:\r\n" );
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document.write( "C(100N,5) = \"%28%28100N%29%28100N-1%29%28100N-2%29%28100N-3%29%28100N-4%29%29%2F5%21\"\r\n" );
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document.write( "So the probability is\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%28400N-4%29%2F5%21\"÷\"%28%28100N%29%28100N-1%29%28100N-2%29%28100N-3%29%28100N-4%29%29%2F5%21\"\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%28400N-4%29%2F5%21\"×\"5%21%2F%28%28100N%29%28100N-1%29%28100N-2%29%28100N-3%29%28100N-4%29%29\"\r\n" );
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document.write( "\"++%2825N%29%2825N-1%29%2825N-2%29%2825N-3%29%2A%28400N-4%29%2Fcross%285%21%29\"×\"cross%285%21%29%2F%28%28100N%29%28100N-1%29%28100N-2%29%28100N-3%29%28100N-4%29%29\"\r\n" );
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document.write( "The first fraction is \"%2825N%29%2F%28100N%29\", exactly \"1%2F4\".  \r\n" );
document.write( "If N is large the next three are also very nearly \"%2825N%29%2F%28100N%29\"\r\n" );
document.write( "or \"1%2F4\", and the last fraction is very nearly \"%28400N%29%2F%28100N%29\", or 4.\r\n" );
document.write( "So that is very nearly\r\n" );
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document.write( "\"%281%2F4%29%281%2F4%29%281%2F4%29%281%2F4%29%284%29\"\r\n" );
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document.write( "\"%281%2F4%29%281%2F4%29%281%2F4%29%281%2Fcross%284%29%29%28cross%284%29%29\"\r\n" );
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document.write( "\"%281%2F4%29%5E3\"\r\n" );
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document.write( "\"1%2F64\"\r\n" );
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document.write( "That's not exact, but it is very close if N is large.\r\n" );
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document.write( "Edwin
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