Statistics :-( can i use a binomial probability?

[conquertheworld5]

Homework Statement

You've got N marbles, and N bins. one by one, a marble is randomly placed in a bin. What is the probability that there will be no marbles in a given bin.

Homework Equations

P=N!/(n1!n2!)*p^n1*q^n2 : binomial probability

The Attempt at a Solution

since we're only interested in whether or not a marble goes into the bin, can I use the binomial distribution? success would be when a marble is placed in a bin other than the bin of interest, and failure would be when a marble is placed in the bin of interest.

n1=N (success), n2=0 (failure)
p=probability of placing a single marble in a bin other than the bin of interest
= (N-1)/N
q=probability of placing a single marble in the bin of interest
= 1/N

P=N!/(N!0!)*p^N*q^0=((N-1)/N)^N

so, what do you think? I've been doing extra stat/probability problems to help with my stat/thermo physics class and I don't have the answers to the questions...

 

[Dick]

I think that's correct. The probability that any given marble doesn't fall in the bin is (N-1)/N. The probability that N of them don't is ((N-1)/N)^N.