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A standard six-sided die is rolled $8$ times.  You are told that among the rolls, there was two $1$'s, two $2$'s, two $3$'s, and two $4$s.  How many possible sequences of rolls could there have been?  (For example, $2,$ $1,$ $3,$ $4,$ $2,$ $1$, $3$, $4$ is one possible sequence.)

 Oct 19, 2024
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There are 8 rolls = 8! = 40320 possible combinatins  IF htere were no duplicate numbers

  BUT there is   two 1's   two 2 's   two 3's  and two 4's    so you have to divide that result by  2!  2! 2! 2! 

to get   40320 / 16 = 2520 possible sequences  

 Oct 19, 2024

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