document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388358>Question 388358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a man has eight pens. Four are black, three are blue, and one is red. How many different ways can the man choose one pen of each color to put in his pocket and carry around with him?<BR>\n" );
document.write( "b)how many ways can the man line up or arrange the eight pens on his desk? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #274700 by </B><A HREF=/tutors/aboutme.mpl?userid=gotpork1><B>gotpork1(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gotpork1><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=274700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm out of practice in data, but hopefully I can help\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a)How many different ways can the man choose one pen of each color to put in his pocket and carry around with him?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since it asked for 1 of each color, we must find the possible ways for each seperate color\r<BR>\n" );
document.write( "\n" );
document.write( "Black: 4P1<BR>\n" );
document.write( "Blue:  3P1<BR>\n" );
document.write( "Red:   1P1\r<BR>\n" );
document.write( "\n" );
document.write( "Since the events are non mutually exclusive, we need to find the solutions for black AND blue AND red:   <BR>\n" );
document.write( "=(4P1)*(3P1)*(1P1)<BR>\n" );
document.write( "=(4)*(3)*(1)<BR>\n" );
document.write( "=12\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)how many ways can the man line up or arrange the eight pens on his desk?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because the 8 pens are not unique elements, and we are looking for the amount of unique ways to arrange, we have to consider how many of each color there are in our solution.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total ways of arranging : = 8!   or  40320<BR>\n" );
document.write( "ways of arranging red: 1<BR>\n" );
document.write( "ways of arranging blue: 3!  or 6<BR>\n" );
document.write( "ways of arranging black: 4!  or  24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So when we are writing the final equation, we get something like this\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=%288%21%29%2F%283%21%2A4%21%29 ALIGN=MIDDLE  ALT=\"R=%288%21%29%2F%283%21%2A4%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );