document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193917>Question 1193917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lucinda goes to the local pizzeria for dinner with a group of friends. The menu offers 4 types of soup, 5 main meals, 6 desserts and 3 different types of drinks. Lucinda will order 2 different courses and a drink. How many dinner options does she have?\r<BR>\n" );
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document.write( "Textbook answer is 222.\r<BR>\n" );
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document.write( "Can someone explain the solution of this problem?\r<BR>\n" );
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document.write( "I thought of <BR>\n" );
document.write( "4*5*6 = 120 (for the first course)<BR>\n" );
document.write( "3*4*5 = 60 (for the second course)<BR>\n" );
document.write( "then i add them up to 180 and multiply it by 3 to get 540.  </SPAN>\n" );
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document.write( "Define these three events<BR>\n" );
document.write( "A = orders a soup<BR>\n" );
document.write( "B = orders a main meal<BR>\n" );
document.write( "C = orders a dessert\r<BR>\n" );
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document.write( "The notation AB means she orders a soup and a main meal.<BR>\n" );
document.write( "For the case AB, there are 4 soups and 5 main meals giving 4*5 = 20 different outcomes here.<BR>\n" );
document.write( "Imagine we had a table with 4 rows to represent the four different soups. Also, this table has 5 columns to represent the different main meals. There would be 4*5 = 20 inner cells to represent all possible soup & main meal combos. This is the reason why we multiply.\r<BR>\n" );
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document.write( "For case AC (soup+dessert), there are 4*6 = 24 outcomes\r<BR>\n" );
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document.write( "For case BC (MainMeal+dessert) there are 5*6 = 30 outcomes.\r<BR>\n" );
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document.write( "We have <BR>\n" );
document.write( "AB+AC+BC = 20+24+30 = 74 ways to have Lucinda pick two different courses.<BR>\n" );
document.write( "Something like AA, BB, or CC aren't allowed because she would order the same type of item (perhaps even two identical items) which isn't allowed.<BR>\n" );
document.write( "She's only allowed 2 selections, and they must be different items. Admittedly the instructions are weirdly worded. \r<BR>\n" );
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document.write( "If she orders one drink (among 3 possible), and two different courses, then there are 3*74 = 222 different dinner options.<BR>\n" );
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