+55 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.
+526 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.
