Balls of ten different colours labeled by a = 1, 2, ... , 10 are to be distributed among different coloured boxes. A ball can only go in a box of the same colour, and each box can contain at most one ball. Let n_a and N_a denote, respectively, the numbers of balls and boxes of colour a . Assuming that N_a >> n_a >> 1, the total entropy (in units of the Boltzmann constant) can be best approximated by