Dwayne plays five games of rock-paper-scissors. In order to seem unpredictable, he never chooses the same move (rock, paper, or scissors) twice in a row. How many different sequences of moves can Dwayne go through?
First, in this problem, you would assume that there are five numbers to multiply since Dwayne played 5 games.
In the first blank, he could choose any move, and there are three, rock, paper, and scissors. In the first blank, you would put 3. Then, since you already picked one, you can't repeat it, so you would end up with 2 for the second blank. Continuing with the next blanks, the third, fourth, and fifth spaces would be 2 choices because you cannot have the one choice you chose previously. In the end, the blanks would look somewhat like this:
3 2 2 2 2
And you would multiply all the numbers.
3 x 2 x 2 x 2 x 2
= 6 x 8