Balls in a box probabilities
Please help me out, I have no idea how to approach this problem...
A box is filled out by 1000 balls. the box can be thought as containing V sites and V balls, with V=1000. The box is repeatedly shaken, so that each ball has enough time to visit all 1000 sites. The ball are identical, except for being uniquely numbered (1-1000).
What is the probability that all of the balls labeled 1-100 lie in the left hand side of the box?
What is the probability that exactly P of the balls labeled 1-100 lie in the left hand side of the box?
Using Stirling's approximation, show that this probability is approx. Gaussian. Calculate the mean of P. calculate the root mean square fluctuations of P about the mean. Is the Gaussian approximation good?