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Tiles numbered 1-6 are each placed randomly into one of three different boxes?

Could you help me explain this math probability problem? Tiles numbered 1-6 are each placed randomly into one of three different boxes. What is the probability that each box contains 2 tiles? Express your answer in a common fraction. I have the answer (10/81) from the textbook but I don't know how it was calculated

various possible patterns & the # of ways of selecting & arranging are :

6-0-0 : 6c6 * 3!/2! = 3
5-1-0 : 6c5 * 3! = 36
4-2-0 : 6c4 *3! = 90
4-1-1 : 6c4*2c1 * 3!/2! = 90
3-3-0 : 6c3 *3!/2! = 60
3-2-1 : 6c3*3c2 *3! = 360
2-2-2 : 6c2*4c2 *3!/3! = 90
total ......................729

reqd. probability
= 90/729
= 10/81
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