document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201878>Question 1201878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A BAG CONTAINS EIGHT CHIPS<BR>\n" );
document.write( "NUMBERED 1 THROUGH 8. TWO CHIPS<BR>\n" );
document.write( "ARE DRAWN RANDOMLY THE BAG AND<BR>\n" );
document.write( "LAID DOWN IN THE ORDER THEY WERE<BR>\n" );
document.write( "DRAWN. WHAT IS THE PROBABILITY<BR>\n" );
document.write( "THAT THE 2-DIGIT NUMBER FORMED IS<BR>\n" );
document.write( "DIVISIBLE BY 3?<BR>\n" );
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document.write( "Answer: <font color=red size=4>5/14</font><BR>\n" );
document.write( "5/14 = 0.357143 approximately\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "If the chip labeled \"1\" is selected 1st, then here are the other possible choices for the 2nd chip: 2,3,4,5,6,7,8<BR>\n" );
document.write( "Once the chip is selected, we don't put it back.\r<BR>\n" );
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document.write( "Of those remaining choices only {2,5,8} will form a two digit number that starts with 1 and is a multiple of 3.<BR>\n" );
document.write( "Those numbers being: 12, 15, 18<BR>\n" );
document.write( "Notice the gap of 3 between adjacent terms.<BR>\n" );
document.write( "Furthermore, notice the sum of the digits of any value gives 3 or a multiple of 3<BR>\n" );
document.write( "1+2 = 3<BR>\n" );
document.write( "1+5 = 6<BR>\n" );
document.write( "1+8 = 9\r<BR>\n" );
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document.write( "If \"2\" was chosen first, then we could have any of these as the 2nd selection {1,4,7}. Again note the gap of 3 between terms.<BR>\n" );
document.write( "21 --> 2+1 = 3<BR>\n" );
document.write( "24 --> 2+4 = 6<BR>\n" );
document.write( "27 --> 2+7 = 9<BR>\n" );
document.write( "That shows we have multiples of 3.\r<BR>\n" );
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document.write( "This process is carried out for the remaining two digit numbers. <BR>\n" );
document.write( "It might be faster to look at a multiplication table, or rely on your memorization of multiples of 3, to quickly get the values we want.<BR>\n" );
document.write( "Keep in mind that<ul><li>Repeat digits aren't allowed. Something like \"33\" won't work.</li><li>We can't form numbers with the digit \"0\" in them (this chip label does not exist). This will rule out something like \"30\".</li><li>We can't form numbers with the digit \"9\" in them (this chip label does not exist either). This rules out something like \"39\".</li></ul>Here is the list of all two digit numbers that are multiples of 3, and that follow the criteria listed above<BR>\n" );
document.write( "12, 15, 18, 21, 24, 27, 36, 42, 45, 48, 51, 54, 57, 63, 72, 75, 78, 81, 84, 87\r<BR>\n" );
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document.write( "There are 20 items in that list<BR>\n" );
document.write( "This is out of 8*7 = 56 different two digit numbers possible that follow the criteria mentioned earlier.\r<BR>\n" );
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document.write( "20/56 = (4*5)/(4*14) = <font color=red>5/14</font> is the final answer as a fraction.\r<BR>\n" );
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document.write( "5/14 = 0.357143 approximately<BR>\n" );
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