Question 4
Three people $A,B,C$ play a game of passing a basketball from one to another. Find the number of ways of passing the ball starting with $A$ and reaching $A$ again on the $11$th pass. For example, one possible sequence is
$$A\to B\to A\to B\to C\to A\to B\to C\to B\to C\to B\to A.$$
$$A\to B\to A\to B\to C\to A\to B\to C\to B\to C\to B\to A.$$