# X red balls indistinguishable and Y green balls indistinguishable

Let's say we have 10 (X) red balls and 3 (Y) green balls. All the balls are indistinguishable.

Firstly, does "indistinguishable" mean that the order of the balls doesn't matter since they do not have a number?

Secondly :

1. How many ways can we place these 13 balls in a line?
2. How many ways can we place these 13 balls in a line, if only their color matters?
3. How many ways can we choose 3 red balls and 2 green balls?

For the question number one, I think it is $$13!$$ For two other questions, I have no idea. I do not grasp the reasoning, the logic behind.

What if we have K colors?

• All 13 can't possibly be indistinguishable with two different colors, unless you are visualising a scenario such as that of total darkness. Dec 21, 2016 at 14:57
• Then, what is the right term? It may be the professor who wrote the syllabus who isn't very rigourous.
– user397873
Dec 21, 2016 at 14:58
• You probably want to say that all red balls are the same and all green balls as well. You should distinguish red and green. Dec 21, 2016 at 15:18