# Homework Help: Combinatronics Probability help

1. Oct 2, 2008

### squaremeplz

1. The problem statement, all variables and given/known data

If 50 out of 100 senators are chosen at random, what is the probability that each state will be represented?

2. Relevant equations

combinatronics i.e. n choose k

3. The attempt at a solution

I get the folliwng

what I did was, please excuse my poor notation, is the following.

P(A) = (1 1)/(2 1)

(the above are binomial coefficiants where (n k))

(1 1) for the case that 50 of the chosen reps are all from dif states

and (2 1) for picking sens from a different state.

Lets say you pick one from MA same state, your next choice can only be the same state or a different one.

so the probability is 1/2.

I also did (50 50)/(100 50) but the probability is unrealisticly low, like 9.91*10^-30

thanks!

2. Oct 3, 2008

### jhicks

Re: Probability

Doesn't seem THAT low, but it's fairly low. Think about it:

The first choice is a gimme, any senator will be from a state you haven't chosen yet. For the second choice, 98/99 senators will get you a new state, then 96/98 and so on. You choose 50 senators out of 100 and what are your choices each of those 50 times?