document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=213282>Question 213282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> it would be greatly appreciated if someone helped with the steps on this one..<BR>\n" );
document.write( "the answer for a) is 95 040 and the answer for b) is 7920\r<BR>\n" );
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document.write( "Twelve different portraits are in the Ling family's collection<BR>\n" );
document.write( "a) In how many ways could five of them be hung in a row on the living room wall?\r<BR>\n" );
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document.write( "b)If Grandma Ling's picture must be included and must be hung in the middle of the group of five, how many different arrangements are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #161118 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=161118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)<BR>\n" );
document.write( "when the problem says \"How many ways\" it<BR>\n" );
document.write( "is implying that order makes a difference<BR>\n" );
document.write( "since the order you see is a different<BR>\n" );
document.write( "\"way\" to hang them.<BR>\n" );
document.write( "When order makes a difference, what you want<BR>\n" );
document.write( "is the Permutation of n objects taken k<BR>\n" );
document.write( "at a time.<BR>\n" );
document.write( "In this problem it is 12 objects taken 5 at a time<BR>\n" );
document.write( "which equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%21+%2F+%2812+-+5%29%21+=+%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F7%21 ALIGN=MIDDLE  ALT=\"12%21+%2F+%2812+-+5%29%21+=+%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F7%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%287%2A6%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2812%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%287%2A6%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2A11%2A10%2A9%2A8+=+95040 ALIGN=MIDDLE  ALT=\"12%2A11%2A10%2A9%2A8+=+95040\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b)<BR>\n" );
document.write( "Now the problem wants to treat 1 picture diffently from the rest<BR>\n" );
document.write( "It will always be in the middle of the group of 5<BR>\n" );
document.write( "Imagine that you have thousands of rooms. Now imagine that you hang all the<BR>\n" );
document.write( "possible arrangements of the other 11 pictures in groups of<BR>\n" );
document.write( "4 in each of the rooms (You've got a huge warehouse full of pictures)<BR>\n" );
document.write( "Imagine that you leave a space in the middle of each group of<BR>\n" );
document.write( "4 to put Grandma's picture in later.<BR>\n" );
document.write( "the number of rooms you need for a different arrangement<BR>\n" );
document.write( "in each room is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%21+%2F+%2811+-+4%29%21 ALIGN=MIDDLE  ALT=\"11%21+%2F+%2811+-+4%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29+%2F+%287%2A6%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%2811%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29+%2F+%287%2A6%2A5%2A4%2A3%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2A10%2A9%2A8+=+7920 ALIGN=MIDDLE  ALT=\"11%2A10%2A9%2A8+=+7920\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "Now just put Grandma's picture in all the empty middle spaces\r<BR>\n" );
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document.write( " </SPAN>\n" );
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