+4 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.)
+57 So, we first start off by calculating C(6,3) which is 20. This is to choose 3 different rolls out of 6 to get the number of 3's. Next, we calculate C(3, 2) which is 3. Since the 3's already took 3 places, there are only three places to put our 2's. We have already placed 5 numbers so now there's only 1 spot left for 1 number, so C(1, 1) is 1. We can multiply 20 by 3 to get 60 possible sequences.
