If the word were, say, MONKEY instead of CANADA, the answer would be 6! arrangements. because MONKEY has all different letters. If we could tell the A's apart in CANADA, say, if it were CANADA, the answer would also be 6! ways. But there are fewer ways than that, because we can't tell the difference between the A's. Let's select a typical arrangement of CANADA, say, NDAACA. Of the 6! arrangments of CANADA. these 6 would all be counted separately among the 6! NDAACA NDAACA NDAACA NDAACA NDAACA NDAACA So just like NDAACA, every other arrangement is counted 6 times among the 6!, too. The reason it is 6 times too many is because in every arrangement there are 3 places to put the red A times 2 places to put the green A times 1 place to put the blue A. That's 3! or 6 places to put the 3 A's. So since the 6! counts each arrangement 3! or 6 times too many, we must divide the 6! by 3! : 6! 6·5·4·3·2·1 —— = ——————————— = 6·5·4 = 120 3! 3·2·1 Answer: 120 ways. Edwin