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.**

BigBoiChungus Jun 26, 2021

#1**+3 **

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.

amygdaleon305 Jun 26, 2021