document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182241>Question 1182241</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I just need someone to check my answers for these questions. Thank You.\r<BR>\n" );
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document.write( "1. In how many different ways can seven books be arranged on a shelf of two particular books must always be next to each other?<BR>\n" );
document.write( " for this I did 5! * 2! * 6 (5! from the 5 left over books and 2! from the two books, 6 positions for the girls to start with)\r<BR>\n" );
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document.write( "2. How many ways can five pieces of candy be divided between two children if each child receives at least one piece of candy?<BR>\n" );
document.write( "There are two cases for this question.<BR>\n" );
document.write( "1st case: <BR>\n" );
document.write( "One child gets one candy, and they other one gets the rest. So<BR>\n" );
document.write( "I did 5 choose 1 times 5 choose 4 which is 25 ways.\r<BR>\n" );
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document.write( "2nd case:<BR>\n" );
document.write( "one child get 2 candies, while the other one get 3.<BR>\n" );
document.write( "So I did 5 choose 2 times 5 choose 3, which is 100 ways.\r<BR>\n" );
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document.write( "Finally I add these values up 100 + 25 = 125\r<BR>\n" );
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document.write( "2. A team of five is to be chosen from a group of eight students. The two tallest students cannot both be on the team. How many different teams can be formed?<BR>\n" );
document.write( " for this one, I did 8 choose 5 minus 6 choose 3 (because the two tallest are removed), which equals t0 56 - 20 = 36. \r<BR>\n" );
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document.write( "3. A group of 8 people consists of 6 adults and two children. Calculate the number of ways in which five people can be selected from these 8 in each of the cases:<BR>\n" );
document.write( "(a)order of selection is unimportant<BR>\n" );
document.write( "(b)the five people are selected in a definite order (I don't understand this one)<BR>\n" );
document.write( "(c)order of selection is unimportant and at most one child may be selected.\r<BR>\n" );
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document.write( "for (a) I did 8 choose 5. 56 ways.<BR>\n" );
document.write( "(b) I don't understand b at all<BR>\n" );
document.write( "(c) I did 7 choose 4 because, one child is guaranteed to be selected. 35 ways.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812206 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52788)</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=812206\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "In this my post, &nbsp;I will solve and explain you &nbsp;ONLY &nbsp;ONE &nbsp;problem of several posted.\r<BR>\n" );
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document.write( "It is the problem n.2 about candies.\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( "        In how many ways can five pieces of candy be divided between \r\n" );
document.write( "        two children if each child receives at least one piece of candy?\r\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( "In this problem, candies are considered as NON-DISTINGUISHABLE - - - so the only difference \r\n" );
document.write( "between different cases is in the NUMBER of candies each child get.\r\n" );
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document.write( "Without going into high and complicated Math, we can write the FULL LIST of all possible solutions/answers\r\n" );
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document.write( "      T   A   B   L   E\r\n" );
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document.write( "    1st child    2nd child\r\n" );
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document.write( "       1            4\r\n" );
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document.write( "       2            3\r\n" );
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document.write( "       3            2\r\n" );
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document.write( "       4            1\r\n" );
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document.write( "It is the set of all possible different solutions.\r\n" );
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document.write( "<U>ANSWER</U>.  There are 4 (four)  different solutions according to 4 different lines in the Table.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Please &nbsp;DO &nbsp;NOT &nbsp;POST many &nbsp;(more than one) &nbsp;PROBLEMS &nbsp;PER &nbsp;POST.\r<BR>\n" );
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document.write( "Post your problems &nbsp;SEPARATELY.\r<BR>\n" );
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document.write( "It is the rule and the policy of this forum.\r<BR>\n" );
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document.write( "Each your problem/question requires to give you a small lesson/lecture, &nbsp;and<BR>\n" );
document.write( "if some tutor will answer everything in one piece, &nbsp;you will get a mess.\r<BR>\n" );
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document.write( "It is why the requirement &nbsp;\"one problem per post\" &nbsp;is established.\r<BR>\n" );
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document.write( "Come again and enjoy my teaching &nbsp;(&nbsp;!&nbsp;)\r<BR>\n" );
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document.write( "By the way, &nbsp;if the candies are considered as &nbsp;DISTINGUISHABLE &nbsp;in this problem, then the answer is &nbsp;&nbsp;30:\r<BR>\n" );
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document.write( "      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;there are 30 different solutions in this case.\r<BR>\n" );
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document.write( "30 = 32 -2;  &nbsp;&nbsp;32 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5 ALIGN=MIDDLE  ALT=\"2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp;:  &nbsp;&nbsp;there are  &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E5 ALIGN=MIDDLE  ALT=\"2%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;&nbsp;different subsets of the set of &nbsp;5 &nbsp;candies\r<BR>\n" );
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document.write( "(which the 1st child get; &nbsp;and then the &nbsp;2nd child gets the rest just without a choice). \r<BR>\n" );
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document.write( "And we subtract &nbsp;2 &nbsp;from &nbsp;32 &nbsp;to exclude the degenerated &nbsp;(and prohibited) &nbsp;cases when one child gets &nbsp;0 &nbsp;(zero) &nbsp;or all &nbsp;5 &nbsp;candies.\r<BR>\n" );
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