document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182133>Question 1182133</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I just need someone to confirm my answers for these questions (if I'm wrong someone please help and correct me thank you:\r<BR>\n" );
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document.write( "In one section of a math test paper, a student answers 3 out of 4 questions in that section. In How many ways can this section be answered if different orders in which the questions are answered count as different ways.\r<BR>\n" );
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document.write( "My answer is 4*3*2 = 24\r<BR>\n" );
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document.write( "In how many ways can 4 boys and 2 girls seat themselves in a row if<BR>\n" );
document.write( "(a)	the 2 girls are to seat next to each other<BR>\n" );
document.write( "(b)	the 2 girls are not to seat to each other<BR>\n" );
document.write( "(c)	the 2 girls are to be separated by 2 boys between them \r<BR>\n" );
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document.write( "for (a) I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.\r<BR>\n" );
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document.write( "for (b) I did 6! - 2!(6-2+1)! = 480\r<BR>\n" );
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document.write( "for (c) I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)\r<BR>\n" );
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document.write( "in how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if <BR>\n" );
document.write( "(e)	no repetition of digits is allowed<BR>\n" );
document.write( "(d)	repetition of digits is allowed\r<BR>\n" );
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document.write( "for (e) I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)\r<BR>\n" );
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document.write( "for (d) i did 5*5*5*5*5\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 #812121 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812121\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "In one section of a math test paper, a student answers 3 out of 4 questions in that section. In How many ways can this section be answered if different orders in which the questions are answered count as different ways.<BR>\n" );
document.write( "My answer is 4*3*2 = 24<br><BR>\n" );
document.write( "Correct<br><BR>\n" );
document.write( "In how many ways can 4 boys and 2 girls seat themselves in a row if<br><BR>\n" );
document.write( "(a) the 2 girls are to seat next to each other<BR>\n" );
document.write( "I did 4!*2!*6 ( 4! is for the boys, 2! for the girls and 6 positions the girls can start at). This for me is a bit tricky for some reason.<br><BR>\n" );
document.write( "Not quite. There are only 5 places the girls can start at. So 4!*2!*5 = 240.<br><BR>\n" );
document.write( "Alternatively....<BR>\n" );
document.write( "Treat the 2 girls as one unit; there are then 5 things to be arranged, and there are 2 different arrangements in one of those things: (5!)(2)=240.  Same answer by a different method.<br><BR>\n" );
document.write( "(b) the 2 girls are not to seat to each other<BR>\n" );
document.write( "I did 6! - 2!(6-2+1)! = 480<br><BR>\n" );
document.write( "Correct.<br><BR>\n" );
document.write( "(c) the 2 girls are to be separated by 2 boys between them<BR>\n" );
document.write( "I did 4! * 2! * 3 (4! from the boys. 2! from the girls and 3 from the fact that there are only 3 cases of this that can be happened)<br><BR>\n" );
document.write( "Correct.<br><BR>\n" );
document.write( "In how many ways can 5-digit numbers be formed using the digits 0,1,3,4,5 if<BR>\n" );
document.write( "(e) no repetition of digits is allowed<BR>\n" );
document.write( "I did 4*4*3*2*1 = 96 (4 at first because zero is not allowed in the first digit of a number)<br><BR>\n" );
document.write( "Correct.<br><BR>\n" );
document.write( "(d) repetition of digits is allowed<BR>\n" );
document.write( "I did 5*5*5*5*5<br><BR>\n" );
document.write( "Not quite; I think you know why. (Look at your answer for (e))<br><BR>\n" );
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