Gift Wrap Combinations

Date: 04/20/99 at 23:12:15
From: Matthew
Subject: Multiplying

This is the problem. I think I should add but my mom said to multiply.  
My answer is 5 and my mom's answer is 6.  Am I right or is my mom?

The problem:

Mary is wrapping a gift. She has 3 different colors of ribbon and 2 
different colors of wrapping paper.  =How many many different ways can 
she wrap the gift?

Thank you.

Date: 04/21/99 at 10:24:05
From: Doctor Rick
Subject: Re: Multiplying

Hi, Matthew, welcome to Ask Dr. Math!

Let's try it. Let's say Mary has:

red ribbon
green ribbon
yellow ribbon

striped paper
white paper

If she picks ONE of these 5 things to wrap the gift, she has 5 ways to 
do it. But that's not how we usually wrap gifts. (Once my brother 
built a greenhouse for my father, and he wrapped it with a huge ribbon 
but no wrapping paper.) Normally, though, we wrap it in paper AND a 
ribbon.

If Mary does it this way, she has these choices:

  striped paper, red ribbon
  striped paper, green ribbon
  striped paper, yellow ribbon
  white paper, red ribbon
  white paper, green ribbon
  white paper, yellow ribbon

Well, it looks like your mom is right. She has probably wrapped a lot 
of presents, so this was easy for her.

But why do you multiply? We can write the choices as a table, like 
this:

                PAPER:
                striped  white
               +-------+-------+
RIBBON: red    |       |       |
               +-------+-------+
        green  |       |       |
               +-------+-------+
        yellow |       |       |
               +-------+-------+

Mary can put a check in any of the 6 boxes in the table, and that's 
her choice - the row shows which ribbon she picked, and the column 
shows which paper she picked. The number of boxes is 3 rows times 2 
columns = 6 boxes. That's why you multiply.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/