Five people are passing a ball amongst themselves. The ball starts with Alonzo. Each person who has the ball passes it onto someone else. After the eighth pass, the ball returns to Alonzo. Find the number of possible sequences of passes.
The number of possible sequences is 310.
I'll assume that Alonzo does not get the ball any other time
first pass 4 choices
2nd 3 choices
3rd 3 choices
8th 1 Alfonzo
4*3^6 = 2916 possible sequences.