Answer to Question #168884 in Statistics and Probability for xborg

Question

How many ways can you order 3 blue marbles, 4 red marbles, and 5 green marbles in a row? 

Answer 1

All 12 marbles can be arranged (permuted) in 12! ways. Many of these arrangements are identical because same colored marbles are indistinguishable from one another. In order to arrive at only those permutations that are distinct, division is required by each permutation relative to blue, red and green marbles, which are 3!, 4! and 5!, respectively. Thus the number of distinct permutations of these 12 marbles = 12!/(5!)(4!)(3!) = 27,720