Math: counting: multiply or add

Tutoring math 12, you may discuss counting problems.  The tutor offers a quick guide for when to multiply vs when to add.

One question you’re sometimes asked about counting is when you multiply, vs when you add.  The answer is simple.  Consider two events, one of which can happen n ways, while the other can happen m ways.

If the events are both going to happen, then the total number of different ways they can happen is nm; you multiply.  However, if only one of the events will happen, but it could be either one, then there are n + m outcomes; you add in that case.  Let’s consider a couple of examples:

Example 1

Bill is going to order dinner and dessert.  There are five dinner choices and three dessert choices.  How many ways can he order the two courses?

Solution:  We know he will order both, so we multiply to get the total number of possibilities.  He can order the two courses in 5×3 = 15 different ways.

Example 2

On a different night, Bill finds himself at another restaurant.  Being in a hurry, he will just order dinner.  There are seven meat choices and three vegetarian choices.  Looking at the menu, Bill is not yet sure whether he will go meat or vegetarian tonight.  How many possible orders could he give for dinner?

Solution:  Bill will only order one dinner.  However, he could go either meat or vegetarian.  Since we don’t know which, we must add the possibilities to get the total. He could order dinner in 7+3 10 different ways.

These counting rules are simple, yet they clarify a good many problems that might seem harder at first.  Good luck with your counting problems:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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