+1520 A standard six-sided die is rolled $7$ times. You are told that among the rolls, there was one $1,$ one $2$, one $3$, one $4$, one $5$, and two $6$s. How many possible sequences of rolls could there have been? (For example, 2, 3, 4, 6, 6, 1, 5 is one possible sequence.)
+1952 First, we need to calculate the total possible number of rolls. Since the dice is rolled 7 times, we have 7! total rolls.
However, since there are duplicates with two 6s being rolled, we must divide by 2! to avoid overcounting.
Thus, we just have
So the answer is 2520.
Thanks! :)
