document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186814>Question 1186814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 4 sets of balls numbered 1 through 5 placed in a bowl. If 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817796 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution from the other tutor shows finding the answer using the C(n,r) formula.<br><BR>\n" );
document.write( "There is another basic method that obtains the answer with far less work.<br><BR>\n" );
document.write( "Consider drawing the 4 balls from the bowl one at a time....<br><BR>\n" );
document.write( "(1) first ball -- there are 20 balls in the bowl; we can pick any of them; P=20/20<BR>\n" );
document.write( "(2) second ball -- there are 19 balls left, of which 3 match the first ball; P=3/19<BR>\n" );
document.write( "(3) third ball -- there are 18 balls left, of which 2 match the first ball; P=2/18<BR>\n" );
document.write( "(4) fourth ball -- there are 17 balls left, of which only 1 matches the first ball; P=1/17<br><BR>\n" );
document.write( "The probability of drawing four matching balls is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F20%29%283%2F19%29%282%2F18%29%281%2F17%29+=+1%2F969 ALIGN=MIDDLE  ALT=\"%2820%2F20%29%283%2F19%29%282%2F18%29%281%2F17%29+=+1%2F969\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 1/969<br>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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