Probability Problem

Question

There are 9 players on a basketball team. For a team photo, 4 of the players are seated on a row of chairs and 5 players stand behind them. In how many different ways can 4 players be aranged on the row of chairs?

Answer 1

for chair 1 you choose from 4 players

for chair 2 you choose from 3 players

for chair 3 you choose from 2 players

for chair 4 you choose from 1 player

4*3*2*1=24 ways

 

suppose you had only 3 players, A,B, and C

ABC

ACB

BCA

BAC

CAB

CBA

now add a fourth player, D

DABC, ADBC, ABDC, ABCD

DACB, ADCB, ACDB, ACDB

continue this with BCA to get 4 more permutations, BAC for 4 more, CAB for 4 more, and CBA for 4 more

you have a total of 4+4+4+4+4+4=24 ways