Question

how many different combinations of 6 volleyball players can be chosen from a pool of 15 players?

Answer 1

15C6

Answer 2

Order doesn't matter, so use the combination formula


nCr = (n!)/(r!(n-r)!)


15C6 = (15!)/(6!*(15-6)!)


15C6 = (15!)/(6!*9!)


15C6 = (15*14*13*12*11*10*9!)/(6!*9!)


15C6 = (15*14*13*12*11*10)/(6!)


15C6 = (15*14*13*12*11*10)/(6*5*4*3*2*1)


15C6 = (3603600)/(720)


15C6 = 5005



So there are 5005 different combinations.