For card players' This problem deals with combinatorial mathematics, illustrated by card distributions. This type of mathematics a essential for the evaluation of entropy in many physical systems A deck of cards consists of N-52 different cards (distinguishable). Before a game of bridge. fa example, the cards are shuffled to obtain a random sequence (distribution). How many distributions ate there with .N cards'? Calculate this number for .N=52. in statistical physics. we are mainly interested in the logarithm of .N and. as derived in Mandl App. A1. a rather precise value is obtained with Sterling's formula for large .V: How .accurate is this formula for .N 52? Show that Sterling's formula is equivalent to What is the accuracy of tins estimate of .N for N=52? A hand in bridge consists of m=13 cards and their sequence is unimportant although it is practical to arrange them. The number of different bands is given by the binomial formula Repeat the argument for this formula. How many different hands can lie dealt in bridge where .N=52 and m=13? Now we wish to divide .V cards into three piles, one with m cards, one with / cards, and one with .N.m-I cards. Piles with 0 caids are at first not considered. In how many Ways can tins be done? We now include the possibility that some of the three numbers could be zero. Does this change the result? this result to an arbitrary number of piles. . M with n, cards in the th pile and N. A game of bridge depends on all four hands. How many different card distributions are there?