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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 27, 2021
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We are finding the number of arrangements of the number "122333".

 

This is equal to \(\frac{6!}{2! \cdot 3!} = \boxed{60}\)

 Feb 27, 2021

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