# Easy Counting Method Problem

• Apr 28th 2011, 07:49 AM
Aryth
Easy Counting Method Problem
I've never really been good at choosing the right method, but here's the problem:

AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?
• Apr 28th 2011, 07:50 AM
TheChaz
Quote:

Originally Posted by Aryth
I've never really been good at choosing the right method, but here's the problem:

AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?

For A, we have two options: in or out.
For B, we have two options:
For C, we have
For D,

What can we conclude?
• Apr 28th 2011, 07:52 AM
alexmahone
Quote:

Originally Posted by aryth
i've never really been good at choosing the right method, but here's the problem:

Annmarie, beau, carlos and dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?

$\displaystyle ^4c_0+^4c_1+^4c_2+^4c_3+^4c_4$
• Apr 28th 2011, 07:56 AM
Aryth
Quote:

Originally Posted by TheChaz
For A, we have two options: in or out.
For B, we have two options:
For C, we have
For D,

What can we conclude?

$\displaystyle 2^4$?

Quote:

Originally Posted by alexmahone
$\displaystyle ^4c_0+^4c_1+^4c_2+^4c_3+^4c_4$

Are you suggesting combinations? That's an odd format.... I'm used to $\displaystyle _4 C _0$... etc.
• Apr 28th 2011, 08:03 AM
alexmahone
Quote:

Originally Posted by Aryth
Are you suggesting combinations? That's an odd format.... I'm used to $\displaystyle _4 C _0$... etc.

Yes; LaTeX is a little flaky at the moment.

Note that you get the answer 16 either way.
• Apr 28th 2011, 08:36 AM
Plato
Quote:

Originally Posted by Aryth
AnnMarie, Beau, Carlos and Dean are four senators on a certain subcommittee. Any or none of them may be selected to another subcommittee. How many different variations for the subcommittee are there?

This is a comment on the other correct replies.
The number of subsets of a set on n elements is $\displaystyle \sum\limits_{k = 0}^n \binom{n}{k} =2^n$.

Note that $\displaystyle 2^4=16$