combination questions

Question

On a soccer team three fullbacks can play any of the three fullback positions, left, center, and right. The three
halfbacks can play any of the three halfback positions, the four forwards can play any of the four positions,
and the goalkeeper plays only his position. How many differentarrangements of the 11 players are possible?

Answer 1

First, find the number of combinations at each position using factorials.

 

Fullback = 3! = 6

Halfback = 3! = 6

Forwards = 4! = 24

Goalkeeper = 1! = 1

 

If you can't understand why to use factorials, draw out all of the combinations by hand. For instance, for the 3 fullbacks our 6 possible combos are:

 

ABC

ACB

BCA

BAC

CBA
CAB

 

So the total combinations for the entire team is all of the combinations at each position multiplied.

 

6 * 6 * 24 * 1 = 864 combinations