document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153447>Question 153447</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?<BR>\n" );
document.write( "2.I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?<BR>\n" );
document.write( "3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?<BR>\n" );
document.write( "4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. <BR>\n" );
document.write( "How many ways can 4 toppings be selected where: <BR>\n" );
document.write( "All the toppings are vegetables<BR>\n" );
document.write( "All the toppings are meat<BR>\n" );
document.write( "There is only cheese on the pizza<BR>\n" );
document.write( "There are 2 vegetables, 1 meat and 1 cheese<BR>\n" );
document.write( "There are 3 meats and 1 cheese.<BR>\n" );
document.write( "What's your favorite combo?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112939 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=112939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. I am going to choose 6 students out of the 15 who currently have A's to be mentors for the students who have C's or lower. How many ways can a group of 6 be selected?<BR>\n" );
document.write( "15C6 = 15!/(16-6)!6! = [15*14*13*12*11*!0] / [1*2*3*4*5*6] = 5005<BR>\n" );
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document.write( "2.I've decided that the mentor group should be made up of 3 girls and 3 boys. Of the students who have A's 9 of them are girls and 6 are boys. How many ways can I form a group of 3 boys and 3 girls?<BR>\n" );
document.write( "9C3 * 6C3 = 84 * 20 = 1680<BR>\n" );
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document.write( "3. State and multi-state lotteries are common in the U.S. To win a typical lottery, you must match 6 numbers between 1 and 40. How many different combinations are possible? What does that say about the chances of winning the lottery?<BR>\n" );
document.write( "40C6 = 3,838,380<BR>\n" );
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document.write( "4. A pizza shop offers the following toppings: 8 different vegetables, 5 different meats, and 4 different cheeses. <BR>\n" );
document.write( "How many ways can 4 toppings be selected where:<BR>\n" );
document.write( " <BR>\n" );
document.write( "All the toppings are vegetables 8C4 = 70<BR>\n" );
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document.write( "All the toppings are meat 5C4 = 5<BR>\n" );
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document.write( "There is only cheese on the pizza 4C4 = 1<BR>\n" );
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document.write( "There are 2 vegetables, 1 meat and 1 cheese<BR>\n" );
document.write( "8C2 * 5C1 * 4C1 = 28 * 5 * 4 = 560<BR>\n" );
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document.write( "There are 3 meats and 1 cheese.<BR>\n" );
document.write( "5C3 * 4C1 = 10*4 = 40<BR>\n" );
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document.write( "What's your favorite combo?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );