_ _ _ _ (4 places for his trophies)

F _ _ _ (3 places left)

F S _ _ (2 places left)

F S B _ (1 place left)

This is why you multiply.

The first trophy can be any of the 4.

The second trophy can be only 3 of the 4.

The third can be 2 of the 4.

The final one can only be one choice.

Multiplying these independent events together, we get :

4*3*2*1 = 24 Combinations

An alternative way to do it would be to draw a tree diagram, which is much more tedious of course.

For example:

Football, Soccer, Bowling, Tennis

Football, Soccer, Tennis. Bowling

Football, Bowling, Tennis Soccer

Football, Bowling, Soccer, Tennis

Football, Tennis, Soccer, Bowling,

Football. Tennis, Bowling, Soccer

then do this for every one.

Hope I could help!!

4 x 3 x 2 x 1 = 4! = 24 possible arrangements

and get 24 different arrangements.