The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Shirts and Pants

Date: 08/29/97 at 22:01:42
From: \The Spark Plug\
Subject: Combinations

Ed has 6 new shirts and 4 new pairs of pants...
How many combinations of shirts and pants does he have?

Is there a formula? I was using 6! and 4! but don't know what to 
with it!

Date: 08/31/97 at 18:49:35
From: Doctor Guy
Subject: Combinations

>Is there a formula?

Yes, there is. Allow me to explain how it is derived. 

Let's call the shirts A,B,C,D,E, and F and the pants w,x,y, and z. 
If Ed chooses shirt A, then what pants could he wear? Any of them, so 
he could wear as follows: Aw, or Ax, Ay, Az. That is 4 combinations. 

We are now finished with shirt A, so let's look at shirt B. He again 
could choose any of the 4 pants, getting Bw,Bx,By, or Bz. That is 
again 4 combinations. 

It would be boring, but we could continue with shirt C, shirt D, 
shirt E, and shirt F. Obviously for each shirt, he has 4 pants to 
choose from. I hope you can see the shortcut: just multiply the 
number of shirts times the number of pants.

Now if he also had 7 different pairs of socks and 3 pairs of shoes, 
and he didn't care what color went with what (some people do care), 
then the total number of combinations would be 

(no. of shirts) * (no. of pairs of pants) * 
(no. of pairs of socks) * (no. of pairs of shoes).

-Doctor Guy,  The Math Forum
 Check out our web site!   
Associated Topics:
High School Permutations and Combinations

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.