document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189691>Question 1189691</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, please help me out with this question. It is very confusing and I don't know how to approach it. \r<BR>\n" );
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document.write( "The tickets for a raffle have four different numbers chosen from 3- 13, with order not important. Determine the probability of winning first prize, which consists of matching all four numbers? \r<BR>\n" );
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document.write( "a. 0.3322% <BR>\n" );
document.write( "b. 0.3%<BR>\n" );
document.write( "c. 29%<BR>\n" );
document.write( "d. 0.3030% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821132 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hi, please help me out with this question. It is very confusing and I don't know how to approach it.<BR>\n" );
document.write( "The tickets for a raffle have four different numbers chosen from 3- 13, with order not important. <BR>\n" );
document.write( "Determine the probability of winning first prize, which consists of matching all four numbers?<BR>\n" );
document.write( "a. 0.3322%<BR>\n" );
document.write( "b. 0.3%<BR>\n" );
document.write( "c. 29%<BR>\n" );
document.write( "d. 0.3030%<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "There are 11 numbers  3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.\r\n" );
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document.write( "In all, there are  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5B11%5D%5E4 ALIGN=MIDDLE  ALT=\"C%5B11%5D%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%29 ALIGN=MIDDLE  ALT=\"%2811%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 330 different combinations of 11 items, taken 4 at a time\r\n" );
document.write( "(330 quadruples).\r\n" );
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document.write( "Only one such combination (quadruple of numbers) provides winning the first prize.\r\n" );
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document.write( "So, the probability is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F330 ALIGN=MIDDLE  ALT=\"1%2F330\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.00303 = 0.3030%  (rounded).\r\n" );
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document.write( "<U>ANSWER</U>.  Option (d).\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "--------------------\r<BR>\n" );
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document.write( "This problem is on COMBINATIONS.\r<BR>\n" );
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document.write( "On Combinations, &nbsp;see introductory lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Combinations-.lesson>Introduction to Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/PROOF-of-the-formula-on-the-number-of-combinations.lesson>PROOF of the formula on the number of Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Problems-on-Combinations.lesson>Problems on Combinations</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Permutations/OVERVIEW-the-lessons-on-Permutations-and-Combinations.lesson>OVERVIEW of lessons on Permutations and Combinations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Combinatorics: Combinations and permutations</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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