document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2229>Question 2229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A teacher wants to write an ordered 5-question test from a pool of 8-questions. How many different forms forms of the test can the teacher write?\r<BR>\n" );
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document.write( "How many 5-number license plates can be made using the digits 1, 2, 3, 4, 5, 6, 7 if an odd digit must come first and  repetitions are allowed? not allowed?\r<BR>\n" );
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document.write( "Suppose in Exercise 2 the license number must be odd. How would it be solved?\r<BR>\n" );
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document.write( "FHow would the number of pernutations of the letters of these words be found?<BR>\n" );
document.write( "1. DEED 2. COMMITTE 3. CINCINNATI 4. SATELLITE 6. MASSACHUSETTS\r<BR>\n" );
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document.write( "A player in a word game has the letters E, E, B, D, G, G , G. In how many ways can these letters be arranged?<BR>\n" );
document.write( "A. 210   B. 1260   C. 840    D. 420\r<BR>\n" );
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document.write( "What is the number of permutations of six numbers on a spinner?\r<BR>\n" );
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document.write( "In how mnay ways can the 10 awimmers on an aquatic ballet team be arranged in a cirurlar pattern?\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 #932 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=932\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the teacher wants all possibilities of 5 questions, even if repeated (just in different order) eg 12345 and 12354 are 2 different versions, then use permutations:\r<BR>\n" );
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document.write( "n=8, r=5, so we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%21%29%2F%28n-r%29%21 ALIGN=MIDDLE  ALT=\"%28n%21%29%2F%28n-r%29%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >...8!/3! = 6720 different combinations of the 8 questions.\r<BR>\n" );
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document.write( "If however, the teacher wants all the combinations of 5 questions where 12345 and 12354 etc are considered the same, then there are 6720/5! = 56.\r<BR>\n" );
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document.write( "2a. odd digit first...4 possibilities,\r<BR>\n" );
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document.write( "so 4 then 7 then 7 then 7 then 7 possibilities with repetitions = 9604\r<BR>\n" );
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document.write( "2b. with repetitions not allowed....\r<BR>\n" );
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document.write( "we have 4 then 6 then 5 then 4 then 3 = 1440.\r<BR>\n" );
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document.write( "3. if number plate was to be odd, its last digit would have to be 1,3,5 or 7, so work that out .\r<BR>\n" );
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document.write( "Jon </SPAN>\n" );
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