document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=625175>Question 625175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me understand how to calculate this.\r<BR>\n" );
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document.write( "Take any Subway restaurant as your experimentation site. Determine the different types of breads, meats, salads, toppings, etc. Find out how many different ways of producing a sandwich/roll. State your assumptions (For example, every sandwich has to have one type of bread but may not include meat).\r<BR>\n" );
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document.write( "11 different ‘vessels’ (Flatbread, or a half or whole of five different breads)(Assume 1 per sandwich)<BR>\n" );
document.write( "4 cheese choices(Assume 0 to 4 per sandwich)<BR>\n" );
document.write( "Toasted or not<BR>\n" );
document.write( "Add bacon or not<BR>\n" );
document.write( "9 different veggies (can range from 0 to any combination of the nine)<BR>\n" );
document.write( "9 different sauces (can range from 0 to any combination of the nine)\r<BR>\n" );
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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 #393399 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=393399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I suspect they asked you how many different sandwiches can be made. (You do not say).<BR>\n" );
document.write( "It is a weird situation, with a lot of possible options.<BR>\n" );
document.write( "Some monster sandwiches can be generated.<BR>\n" );
document.write( "Your problem hints about 11 different choices for the bread. (I imagine flatbread has just one option, but for the other 5 types of bread you can use one of half. Online, I saw 10 options, including flat bread and four types of roll in 6-inch or foot long sizes).<BR>\n" );
document.write( "Then, there are options for the filling flavor. Online, I saw 5 breakfast-type flavors. I would ignore those to make it simpler. There were 20 options for flavor for lunch-type sandwiches, including \"veggie delite\" and 19 with some type of meat. I would stick to those 20 options. <BR>\n" );
document.write( "There are more choices that are yes/no type:<BR>\n" );
document.write( "bacon?<BR>\n" );
document.write( "onion?<BR>\n" );
document.write( "lettuce?<BR>\n" );
document.write( "tomato?<BR>\n" );
document.write( "bell peppers?<BR>\n" );
document.write( "cucumbers slices?<BR>\n" );
document.write( ".......<BR>\n" );
document.write( "mayo?<BR>\n" );
document.write( "lite mayo?<BR>\n" );
document.write( "oil?<BR>\n" );
document.write( "ranch?<BR>\n" );
document.write( "chipotle southwest?<BR>\n" );
document.write( "honey mustard?<BR>\n" );
document.write( "mustard?<BR>\n" );
document.write( ".....<BR>\n" );
document.write( "Your problem talks about 9 veggie choices and 9 sauce choices. Online, I saw 9 sauces, but only the 5 veggies I listed above.<BR>\n" );
document.write( "If you had 9 veggie choices and 9 sauce choices, and you could ask for none or as many as you wish, there would be 2 possibilities for each choice: yes or no.<BR>\n" );
document.write( "That would give you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E18 ALIGN=MIDDLE  ALT=\"2%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" > possibilities.<BR>\n" );
document.write( "All choices multiply the possibilities.<BR>\n" );
document.write( "Coupling those <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E18 ALIGN=MIDDLE  ALT=\"2%5E18\"   DISABLED_style= \"max-width:90%; height:auto;\" > \"fixings\" possibilities with 20 filling flavors, and 11 bread choices, plus 2 choices (yes or no) for toasting, the possibilities are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2A20%2A2%2A2%5E19=11%2A20%2A2%5E19 ALIGN=MIDDLE  ALT=\"11%2A20%2A2%2A2%5E19=11%2A20%2A2%5E19\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's about 100 million possible sandwiches.<BR>\n" );
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