Question 1146390: Five students, A, B, C, Dand E, are passing a ball, initially A holds the ball. Given A passes the ball to D at 5th pass, how many possible ways of passing the ball are there?
Answer by greenestamps(13209)   (Show Source):
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The first pass is from A to one of the others; the 5th pass is from A to D. That means the 4th pass is from some player to A.
On the first pass, A can pass to any other player: 4 choices.
On the second pass, the player with the ball can pass to any other player: again 4 choices.
On the third pass, the player with the ball can't pass to himself, and he can't pass to A, because the 4th pass has to go to A: 3 choices.
Then the 4th pass has to go to A (1 choice) and the 5th pass has to go to D (1 choice).
Total number of ways: 4*4*3*1*1 = 48
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