Probability question from DAT destroyer

[joonkimdds]

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There r 3 red, 4 white, and 5 blue balls in a jar. what is the probability of drawing a red, a white and a blue ball without replacement?

I understand that I need to multiply probabibility of each to get the probability of drawing red, white and blue in any combination.
3/12 times 4/11 times 5 /10 is 1/22

then the solution says
"now we must count the number of arrangements: therer r 3 different balls so 3!=3 x2 x 1 = 6"
and then 1/22 x 6 = 3/11 is the answer.

I don't understand why i need to find the number of arrangements and multiply it into the probability of drawing balls. The question only asked for the probability of drawing them and 1/22 is my answer. I am confused why i should go another step.

 

[Law0830]

Very simple in all of these probability questions, you cant infer that the balls came out in a certain order. So even though we got the probability of getting a red white and blue without replacement you dont know the order so thats the 3! because their are three balls. I Actually saw a very similar question on topscore to this one.