document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87096>Question 87096</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i need help with these two problems can someone help me.thanks\r<BR>\n" );
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document.write( "Problem #1<BR>\n" );
document.write( "A group of 7 workers decides to send a delegation of 2 to their supervisor to discuss their greivances.<BR>\n" );
document.write( "a) how many delegations are possible?<BR>\n" );
document.write( "b)If it is decided that  a particular worker must be in the delegation, how many different delegations are possible?<BR>\n" );
document.write( "c)IF there are 2 women and 5 men in the group, how many delegations would include at least 1 woman?\r<BR>\n" );
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document.write( "Problem #2<BR>\n" );
document.write( "A television commercial for Little Caesars<BR>\n" );
document.write( "pizza announced that with the purchase of two pizzas, one<BR>\n" );
document.write( "could receive free any combination of up to five toppings<BR>\n" );
document.write( "on each pizza. The commercial shows a young child waiting<BR>\n" );
document.write( "in line at Little Caesars who calculates that there are<BR>\n" );
document.write( "1,048,576 possibilities for the toppings on the two pizzas.*\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "a. Verify the child’s calculation. Use the fact that Little<BR>\n" );
document.write( "Caesars has 11 toppings to choose from. Assume that the<BR>\n" );
document.write( "order of the two pizzas matters; that is, if the first pizza<BR>\n" );
document.write( "has combination 1 and the second pizza has combination<BR>\n" );
document.write( "2, that is different from combination 2 on the first pizza<BR>\n" );
document.write( "and combination 1 on the second.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b. In a letter to The Mathematics Teacher, Joseph F. Heiser<BR>\n" );
document.write( "argued that the two combinations described in part a<BR>\n" );
document.write( "should be counted as the same, so the child has actually<BR>\n" );
document.write( "overcounted. Give the number of possibilities if the<BR>\n" );
document.write( "order of the two pizzas doesn’t matter.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63080 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=63080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem #1<BR>\n" );
document.write( "A group of 7 workers decides to send a delegation of 2 to their supervisor to discuss their greivances.<BR>\n" );
document.write( "a) how many delegations are possible?<BR>\n" );
document.write( "Answer: 7C2 = 21<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "b)If it is decided that a particular worker must be in the delegation, how many different delegations are possible?<BR>\n" );
document.write( "Answer: 1*6 = 6<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "c)IF there are 2 women and 5 men in the group, how many delegations would include at least 1 woman? <BR>\n" );
document.write( "Answer: # of at least 1 woman pairs = # of pairs - # of 2 man pairs<BR>\n" );
document.write( "# of at least 1 woman pairs = 21 - 5C2 = 21-10 = 11<BR>\n" );
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document.write( "Problem #2<BR>\n" );
document.write( "A television commercial for Little Caesars<BR>\n" );
document.write( "pizza announced that with the purchase of two pizzas, one<BR>\n" );
document.write( "could receive free any combination of up to five toppings<BR>\n" );
document.write( "on each pizza. The commercial shows a young child waiting<BR>\n" );
document.write( "in line at Little Caesars who calculates that there are<BR>\n" );
document.write( "1,048,576 possibilities for the toppings on the two pizzas.* \r<BR>\n" );
document.write( "\n" );
document.write( "a. Verify the child’s calculation. Use the fact that Little<BR>\n" );
document.write( "Caesars has 11 toppings to choose from. Assume that the<BR>\n" );
document.write( "order of the two pizzas matters; that is, if the first pizza<BR>\n" );
document.write( "has combination 1 and the second pizza has combination<BR>\n" );
document.write( "2, that is different from combination 2 on the first pizza<BR>\n" );
document.write( "and combination 1 on the second. <BR>\n" );
document.write( "# of combinations on one pizza = 11C1+11C2+11C3+11C4+11C5 = 1023<BR>\n" );
document.write( "# of combinations on the two pizza = 1023*1023 = 1,046,529<BR>\n" );
document.write( "If order makes a difference you get 2*1046529=2,093,058 \r<BR>\n" );
document.write( "\n" );
document.write( "b. In a letter to The Mathematics Teacher, Joseph F. Heise<BR>\n" );
document.write( "argued that the two combinations described in part a<BR>\n" );
document.write( "should be counted as the same, so the child has actually<BR>\n" );
document.write( "overcounted. Give the number of possibilities if the<BR>\n" );
document.write( "order of the two pizzas doesn’t matter.<BR>\n" );
document.write( "Looks like 1,046,529 to me.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );