# Math Help - Counting methods

1. ## 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.

2. Help anyone?

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3. 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.