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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.)

 

I have tested 120 and 20 as answers, they are incorrect.

 Jun 26, 2021
 #1
avatar+524 
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In order to find the no. of possible sequences, you find the no. of ways 1, 2, 2, 3, 3 and 3 can be arranged. 

So, no. of digits = 6

      no. of 2's = 2

      no. of 3's = 3

 

Possible no. of rolls \(={6!\over 2!×3!}=60\)

 

Hope you got it. 

 Jun 26, 2021

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