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### 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!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Permutations and Combinations

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