Counting methods

• Mar 9th 2009, 07:31 PM
VENI
Counting methods
I'm having trouble thinking about these questions.

(1) How many ways can a committee of $n$ members form two subcommittees if they need not be disjoint and not everyone has to serve?

(2) Find an upper bound on the number of steps to solve a Towers of Hanoi game with 4 towers instead of 3.

Thank you.
• Mar 10th 2009, 02:36 PM
VENI
Help anyone?

Bumping is against the rules of the forum.
• Mar 10th 2009, 03:10 PM
Plato
Quote:

Originally Posted by VENI
(1) How many ways can a committee of $n$ members form two subcommittees if they need not be disjoint and not everyone has to serve?

(2) Find an upper bound on the number of steps to solve a Towers of Hanoi game with 4 towers instead of 3.

1) Assuming that neither of the two subcommittees can be empty the answer is: ${{2^n-1}\choose 2}$.

That is simply the number of ways to select two nonempty subsets from a set of $n$.

I have no idea what 2) is about.

Bumping is against the rules of the forum.