Probability involving a deck of cards

[karthikphenom]

Homework Statement

A deck of 52 playing cards are tosses 1 by 1 into a large box containing 4 sub-compartments. On a given throw, a card is equally likely to fall into any of the sub-compartments. After all 52 cards are thrown into the box, what's the probability of getting these distributions
a) 13-13-13-13
b) 16-22-10-4

I'm bad at doing probability calculations, and I have no idea of how to proceed. Can someone please help me out?

 

[lanedance]

pretty tricky.. and there might be an easier way i haven't though of, but this should at least get you started thinking about it

start with one card what are the possible outcomes & probabilties for each, then try 2 & 3 to get a feel for the problem

then i haven't tried this but then i would consider one box, what is the probability it ends up with "i" cards after the full 52? could use a binomial distribution...

those "i" cards are essentially independent from which other box the others land in, so given (52-i) what's the probablilty the next box gets "j" cards and so on

then consider whether the order of the boxes matter...

you can probably work out the total number of outcomes using something like combinations with repetition