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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.

 Aug 7, 2020
 #1
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The number of possible sequences is 310.

 Aug 7, 2020
 #2
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I'll assume that Alonzo does not get the ball any other time

 

Alfonzo

first pass  4 choices

2nd   3 choices

3rd    3 choices

4th    3

5th    3

6th    3

7th    3

8th    1     Alfonzo

 

4*3^6 = 2916 possible sequences.

 Aug 7, 2020

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