What is the number of non-decreasing functions from A = {1, 2, 3, 4, 5} to B = {-2, -1, 0, 1, 2, 3, 4, 5}?

Level: Senior

This problem is equivalent to finding the number of ways to distribute |A| = 5 identical balls into |B| = 8 different boxes. This, in turn, is equivalent to the number of ways of dividing 5 balls in a line into 8 sections. In other words, it is the number of permutations of 5 balls and 7 dividers, which is (7+5)C5 = 12*11*10*9*8/(5*4*3*2) = 792.