document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=856500>Question 856500</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Permutations<BR>\n" );
document.write( "a) How many ways can 3 people be placed in one line where order is important? This is permutation. <BR>\n" );
document.write( "This is my first time using this site, could you also explain how you would figure this out on a graphics calculator (Texas Instruments TI-84 plus) i.e. what I would need to type in in order to get an answer (nPr?).<BR>\n" );
document.write( "Thank you.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #515964 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=515964\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3 people in a line and you want to figure out how many arrangements are possible .<BR>\n" );
document.write( "that would be 3! which is equal to 3*2*1.<BR>\n" );
document.write( "it is also equal to 3P3 which means choosing 3 people out of 3 where order is important.\r<BR>\n" );
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document.write( "in your ti-84 plus calculator, you would do the following for 3!:<BR>\n" );
document.write( "press 3 then press math then press right arrow 3 times to PRB then enter 4 for ! then press enter.<BR>\n" );
document.write( "you should get 6 because 3! is equal to 3*2*1 which is equal to 6.\r<BR>\n" );
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document.write( "in your ti-84 plus calculator, you would do the following for 3P3:<BR>\n" );
document.write( "press 3 then press math then press right arrow 3 times to PRB then enter 2 for nPr then enter 3 then press enter.<BR>\n" );
document.write( "you should get 6 because 3P3 is equal to 3*2*1 which is equal to 6.\r<BR>\n" );
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document.write( "3! and 3P3 will give you the same answer.<BR>\n" );
document.write( "nPx is usually used for choosing x out of n where order is important.<BR>\n" );
document.write( "x is usually smaller than n but doesn't have to be.<BR>\n" );
document.write( "x can never be greater than n.\r<BR>\n" );
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document.write( "for example:<BR>\n" );
document.write( "4P2 is equal to 4*3 which is equal to 12.\r<BR>\n" );
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document.write( "if order is not important, then use 4C2 which will be equal to (4*3)/2 = 6.\r<BR>\n" );
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document.write( "try these in your calculator.\r<BR>\n" );
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document.write( "in your ti-84 plus calculator, you would do the following for 4P2:<BR>\n" );
document.write( "press 4 then press math then press right arrow 3 times to PRB then enter 2 for nPr then enter 2 then press enter.<BR>\n" );
document.write( "you should get 12 because 4P2 is equal to 4*3 which is equal to 12.\r<BR>\n" );
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document.write( "in your ti-84 plus calculator, you would do the following for 4C2:<BR>\n" );
document.write( "press 4 then press math then press right arrow 3 times to PRB then enter 3 for nCr then enter 2 then press enter.<BR>\n" );
document.write( "you should get 6 because 4C2 is equal to (4*3)/(1*2) which is equal to 6.\r<BR>\n" );
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document.write( "the general formula for nPx is n! / (n-x)!\r<BR>\n" );
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document.write( "in practice, you can do the following:\r<BR>\n" );
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document.write( "assume 10P3\r<BR>\n" );
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document.write( "per the formula this is equal to 10! / (10-3)! which is equal to 10! / 7!\r<BR>\n" );
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document.write( "you carry the numerator down to 7! as shown below:\r<BR>\n" );
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document.write( "10P3 = (10*9*8*7!) / 7!\r<BR>\n" );
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document.write( "the 7! in the numerator and the 7! in the denominator cancel out and you are left with 10*9*8\r<BR>\n" );
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document.write( "notice that the multiplication is for 3 times which is the 3 in the 10P3.\r<BR>\n" );
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document.write( "so the shortcut for 10P3 is 10*9*8, because the 7! in the numerator and the 7! in the denominator will cancel out.\r<BR>\n" );
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document.write( "similarly, the formula for nCx is equal to n! / (n-x)! * x!)\r<BR>\n" );
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document.write( "you can do the same thing as follows:\r<BR>\n" );
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document.write( "assume 10C3.\r<BR>\n" );
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document.write( "this is equal to 10! / ((10-3)! * 3!) which is equal to 10! / (7!*3!)\r<BR>\n" );
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document.write( "you can rewrite this as (10*9*8*7!) / (7!*3!).\r<BR>\n" );
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document.write( "the 7! in the numerator and the 7! in the denominator cancel out and you are left with (10*9*8) / 3! which is equal to (10*9*8) / (1*2*3) which is easier to simplify and find what the number is.\r<BR>\n" );
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document.write( "so the shortcut for 10C3 is equal to (10*9*8)/3!.\r<BR>\n" );
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document.write( "of course, it's always simpler to use the calculator as shown above.<BR>\n" );
document.write( "10P3 is equal to 720<BR>\n" );
document.write( "10c3 is equal to 120\r<BR>\n" );
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document.write( "here's a reference from the web that you should find useful.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://mathbits.com/MathBits/TISection/Algebra1/Probability.htm\" target = \"_blank\">http://mathbits.com/MathBits/TISection/Algebra1/Probability.htm</a><BR>\n" );
document.write( "at the bottom of that page is a link to the table of contents.<BR>\n" );
document.write( "they will look like this:<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://mathbits.com/MathBits/TISection/Openpage.htm\" target = \"_blank\">http://mathbits.com/MathBits/TISection/Openpage.htm</a>\r<BR>\n" );
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