How Many Barbies

Date: 08/11/99 at 21:06:03
From: jun huron
Subject: How many different Barbies can I make?

Dear Dr. Math,

My favorite website is barbie.com where you are able to build your own
Barbie. My question is: how many different Barbies can I make if I 
can choose from 4 different skin colors, 3 different eye colors, 4 
different hairstyles, and 6 different hair colors? 

I thought if I figured out the square root of 4 that would be the 
answer, but that did not make sense completely. My babysitter said the
formula for something called permutations might give me the answer but
I don't understand how and she does not know the formula. 

Please let me know if you know how I can figure this out. If you send 
the formula and answer to my mom she will explain it to me and tell me
if I am wrong or right. Thanks.

Date: 08/12/99 at 10:15:30
From: Doctor Annie
Subject: Re: How many different Barbies can I make?

Hi Jun. Your babysitter is on the right track. Permutations is the 
exact right word! You might try searching the Dr. Math archives for 
questions and answers about permutations if you want to learn more - 
there's a whole page of answers in the high school area at 

  http://mathforum.org/dr.math/tocs/permutations.high.html   

- but I'll give you a brief outline here.

Let's start with the skin color. That gives us 4 different Barbies.  

Now, each of those 4 Barbies could have 3 different eye colors, so we 
multiply 4 x 3 for 12 different Barbies so far.  

Each of those Barbies can have 4 hairstyles, so that's 12 x 4 for
48 different Barbies.  Do you think you can finish the problem?

Similar problems come up when people try to figure out how many 
license plates you can make with certain rules - like if you have five
letters or numbers on a license plate, and the first three have to be 
letters, and the last two are numbers. So there are 26 x 26 x 26 x 10 
x 10 possible license plates - that's a lot! (See if you can figure 
out how I got those numbers.)

Write back if you need some more help, but I hope that makes sense.

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