High school probability question

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"Four six sided dice are thrown. Find the probability that the total score is 6."

Answer is: 5/648

I don't even know where to begin. This question was in our Binomial Probability (BP) homework but I don't know how BP would be applicable here?

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The two cases that need to be considered are {3, 1, 1, 1} and {2, 2, 1, 1} which can be permuted a total of 4C1 + 4C2 = 10 times. Each case has equal probability of (1/6)^4. Multiplying gives the answer.