# Thread: Easy Counting Method Problem

1. ## 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?

2. 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?

3. 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?
$^4c_0+^4c_1+^4c_2+^4c_3+^4c_4$

4. 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?
$2^4$?

Originally Posted by alexmahone
$^4c_0+^4c_1+^4c_2+^4c_3+^4c_4$
Are you suggesting combinations? That's an odd format.... I'm used to $_4 C _0$... etc.

5. Originally Posted by Aryth
Are you suggesting combinations? That's an odd format.... I'm used to $_4 C _0$... etc.
Yes; LaTeX is a little flaky at the moment.

Note that you get the answer 16 either way.

6. 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 $\sum\limits_{k = 0}^n \binom{n}{k} =2^n$.

Note that $2^4=16$