Combination(Repetition) followed by Permutation(Repetition)

Question

No of balls = 3 identical red, 3 identical blue, 4 identical green.

Urns = U1, U2, U3.

Now my doubt here is that we can arrange all these 10 balls in those 3 urns as C(10+3-1, 3-1) or C(10+3-1,10), but consider a urn which has content as 2 red balls and 2 green balls. 

which can be arranged in:-

fact(4)/ { fact(2) * fact(2) } = 6

but in through this formula:-

C(10+3-1, 3-1) 

we are calculating 6 different permutations as 1 in that urn. And similar happening with other urns also.

So, how we can resolve such kind of question?

Comments

urn is just a basket...only thing matter is to place balls inside that urn, arrangement is not required once you have placed balls inside that urn..

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Ok, so instead of urn if take tray where the order of placing the object is matters, then what it will be?

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yes, in that case arrangements also matters..