document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=425928>Question 425928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a probability problem.  If someone can help me figure out the steps and answer, it would be great.  Thank you!\r<BR>\n" );
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document.write( "problem:<BR>\n" );
document.write( "If a mother has three bananas, two pears and two oranges, in how many different ways can she give the fruit to her daughter in one week, one piece of fruit per day? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #296413 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=296413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b = bananas<BR>\n" );
document.write( "p = pears<BR>\n" );
document.write( "o = oranges\r<BR>\n" );
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document.write( "mother has 3b + 2p + 2o\r<BR>\n" );
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document.write( "how many different ways can she serve these fruits in one week?\r<BR>\n" );
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document.write( "i believe your answer will be 7! / (3! * 2! * 2!) = 210\r<BR>\n" );
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document.write( "these are permutations because order is important.\r<BR>\n" );
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document.write( "a simple example can be used to show you how this works.\r<BR>\n" );
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document.write( "suppose it was only 3 days and you had 2b and 1p\r<BR>\n" );
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document.write( "the number of ways would be 3! / (2! * 1!) = 3.\r<BR>\n" );
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document.write( "those ways would be:\r<BR>\n" );
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document.write( "bba<BR>\n" );
document.write( "bab<BR>\n" );
document.write( "abb\r<BR>\n" );
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document.write( "the first column is the first day, the second column is the second day, the third column is the third day.\r<BR>\n" );
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document.write( "a sightly more complex example would be:\r<BR>\n" );
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document.write( "2b + 2p over 4 days\r<BR>\n" );
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document.write( "answer would be 4! / (2! * 2!) = 6\r<BR>\n" );
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document.write( "those ways would be:\r<BR>\n" );
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document.write( "bbpp<BR>\n" );
document.write( "bpbp<BR>\n" );
document.write( "bppb<BR>\n" );
document.write( "pbbp<BR>\n" );
document.write( "pbpb<BR>\n" );
document.write( "ppbb\r<BR>\n" );
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document.write( "an even more complex example would be:\r<BR>\n" );
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document.write( "2b + 2p + 1o in 5 days.\r<BR>\n" );
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document.write( "number of ways would be 5! / (2! * 2! * 1!) = 30\r<BR>\n" );
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document.write( "these would be:\r<BR>\n" );
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document.write( "bbppo<BR>\n" );
document.write( "bbpop<BR>\n" );
document.write( "bbopp\r<BR>\n" );
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document.write( "bpbpo<BR>\n" );
document.write( "bpbop<BR>\n" );
document.write( "bppbo<BR>\n" );
document.write( "bppob<BR>\n" );
document.write( "bpobp<BR>\n" );
document.write( "bpopb\r<BR>\n" );
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document.write( "pbbpo<BR>\n" );
document.write( "pbbop<BR>\n" );
document.write( "pbpob<BR>\n" );
document.write( "pbpbo<BR>\n" );
document.write( "pbopb<BR>\n" );
document.write( "pbobp\r<BR>\n" );
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document.write( "ppbbo<BR>\n" );
document.write( "ppbob<BR>\n" );
document.write( "ppobb\r<BR>\n" );
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document.write( "obbpp<BR>\n" );
document.write( "obpbp<BR>\n" );
document.write( "obppb\r<BR>\n" );
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document.write( "bobpp<BR>\n" );
document.write( "bopbp<BR>\n" );
document.write( "boppb\r<BR>\n" );
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document.write( "opbbp<BR>\n" );
document.write( "opbpb<BR>\n" );
document.write( "oppbb\r<BR>\n" );
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document.write( "pobbp<BR>\n" );
document.write( "pobpb<BR>\n" );
document.write( "popbb\r<BR>\n" );
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document.write( "it gets harder to show you when the numbers get higher.\r<BR>\n" );
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document.write( "trust me on 7! / (3! * 2! * 2!)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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