document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=534794>Question 534794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A box contains 50 balls numbered from 1 to 50. If 10 balls are drawn with replacement, what is the probability that at least two of them have the same number? \r<BR>\n" );
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document.write( "Any help would be appreciated! Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710815 by </B><A HREF=/tutors/aboutme.mpl?userid=Alyrian><B>Alyrian(2)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alyrian><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The previous solution was almost correct with a little flaw in counting.\r<BR>\n" );
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document.write( "So you want the number of permutations of size 10 from 50, with replacement. <BR>\n" );
document.write( "This is just 50^10, or n^r.\r<BR>\n" );
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document.write( "Then you need to find the number of PERMUTATIONS without replacement, as this<BR>\n" );
document.write( "will give you the numbers of ways you can rearrange 10 distinct object picked<BR>\n" );
document.write( "from 50.<BR>\n" );
document.write( "This is 50P10, nPr.\r<BR>\n" );
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document.write( "Then the probability of drawing 10 balls and not getting any matches is <BR>\n" );
document.write( "50P10/50^10\r<BR>\n" );
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document.write( "This is the complement of what you're actually looking for, so subtract this<BR>\n" );
document.write( "value from 1<BR>\n" );
document.write( "1 - 50P10/50^10\r<BR>\n" );
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document.write( "The numerical value is 0.61829331945. </SPAN>\n" );
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