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.)
+506 This is the same as asking to permute the string 333221 in distinguishable ways. That would be equal to 6!=6⋅5⋅4⋅3⋅2, but we're overcounting by a factor of 3!=3⋅2 multiplied by 2!=2, so we need to divide that from the original 6!. That would be equal to 6⋅5⋅4⋅3⋅23⋅2⋅2=60
