In this problem we’ll explore the connection between permutations of multisets, and combinations…
In this problem we’ll explore the connection between permutations of multisets, and combinations in which a set is split into several subsets.
(a) How many permutations are there of the letters ABBCCC?
(b) Suppose there are 6 marbles, labeled with the integers 1 through 6; and 3 boxes, labeled with the letters A, B, and C. In how many ways is it possible to arrange the marbles with 1 marble in box A, 2 marbles in box B, and 3 marbles in box C?
(c) Describe a bijection between the permutations of ABBCCC from part (a) and the arrangements of the marbles 1 through 6 in boxes A, B, and C from part (b).