One question you’re sometimes asked about counting is when you multiply, vs when you add. \u00a0The answer is simple. \u00a0Consider two events, one of which can happen n<\/em><\/strong> ways, while the other can happen m<\/em><\/strong> ways.<\/p>\n If the events are both going to happen, then the total number of different ways they can happen is nm<\/strong>; you multiply. \u00a0However, if only one of the events will happen, but it could be either one, then there are n + m<\/strong><\/em> outcomes; you add in that case. \u00a0Let’s consider a couple of examples:<\/p>\n Example 1<\/strong><\/p>\n Bill is going to order dinner and dessert. \u00a0There are five dinner choices and three dessert choices. \u00a0How many ways can he order the two courses?<\/p>\n Solution:<\/strong> \u00a0We know he will order both, so we multiply to get the total number of possibilities. \u00a0He can order the two courses in 5×3<\/strong><\/em>\u00a0=\u00a015<\/strong> different ways.<\/p>\n Example 2<\/strong><\/p>\n On a different night, Bill finds himself at another restaurant. \u00a0Being in a hurry, he will just order dinner. \u00a0There are seven meat choices and three vegetarian choices. \u00a0Looking at the menu, Bill is not yet sure whether he will go meat or vegetarian tonight. \u00a0How many possible orders could he give for dinner?<\/p>\n Solution:<\/strong> \u00a0Bill will only order one dinner. \u00a0However, he could go either meat or vegetarian. \u00a0Since we don’t know which, we must add the possibilities to get the total. He could order dinner in 7+3\u00a0<\/strong><\/em>=\u00a010<\/strong> different ways.<\/p>\n These counting rules are simple, yet they clarify a good many problems that might seem harder at first. \u00a0Good luck with your counting problems:)<\/p>\n