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# Dice roll

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A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1, two 2's, and three 3's. How many possible sequences of rolls could there have been? (For example, 3,2,3,1,3,2 is one possible sequence.)

Feb 24, 2021

We are basically finding the number of arrangements of the sequence {122333}, which is $$\frac{6!}{2! \cdot3!} = \boxed{60}.$$