A bowl contains many red, orange, and green jelly beans, in equal numbers. You are to make a line of 3 jelly beans by randomly taking 3 beans from the bowl.

VIDEO TRANSCRIPT

This is Giancoli answers with Mr. Dychko. If you have a one red, one orange and one green, there are six different possible micro-states for that macro-state of one each, one of each color. You could have the red one first then the orange one and the green one as shown here or you could have the red one first and then pick a green one second and then orange one last then green one first, red one second, orange one last and so on and so on and there are six possible permutations for this one red one orange and one green. And which also happens to be three factorial by the way and then which means three times two times one. And then if you have a single red in two oranges that's going to be three factorial divided by the number of duplicates factorial. So there's two oranges. So we go divided by two factorial and that gives three. Or you could you right out each possibility of being you know red orange orange or red. Three different places for that red to go so the orange red orange or orange orange red. So that's the way to show it without using factorial is that there are three micro-states here. For red green green, the same idea three micro-states and orange orange green has three micro-states. All three being orange, there's only one way to arrange that. There's one micro-state and then orange green green gets three micro-states, red red green gives three micro-states, green orange orange gives three micro-states and then all green and then all red each have one micro-state possibility and there's 27 in total. so the probability for all being, being green oh… sorry red, it doesn't matter, would be one micro-state for all red divided by a total of 27 micro-states. So, one twenty-seventh. And for two Greens and one orange there are there are three micro-states for that and divided by twenty seven gives one-ninth as its probability.