How many ways can 7 tennis players and their coach be lined up against a wall if the coach must be on one of the ends?

Answer 1

2 * 7! = 10080

Answer 2

There are 7! * 2 = 10,080 ways!

How? Well, let's line up just the players for a moment:

_ _ _ _ _ _ _

There are 7 players who can go in the first position, 6 in the second (since you placed one already!), 5 in the third, and so forth. That leaves us with 7*6*5*4*3*2*1 = 7! = 5,040 different ways just to line up the students.

Now, for each row of students, the coach can either go to the left of the line or the right, so there are 2 choices for the coach. Multiplying these together gives us 7! * 2 = 10,080.