Raynor2i

2022-07-15

All 15 players on the Tall U. basketball team are capable of playing any position.
(a) How many ways can the coach at Tall U. fill the five starting positions in a game?
(b) What is the answer if the center must be one of two players?

Quenchingof

Expert

Step 1
Approach via multiplication principle.
- Pick who the center is: You have two options
- Pick who the power forward is: You have 14 remaining options since it can't be who you picked for the center
- Pick who the small forward is: You have 13 remaining options since it can't be either of the two previously selected people
- Pick who the point guard is: 12 remaining options
- Pick who the shooting guard is: 11 remaining options
Step 2
- The answer then is $2\cdot 14\cdot 13\cdot 12\cdot 11$

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