Question

Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?

Answer 1

220
12C9 = 12!/(12-9)!*9!
= 12*11*10/6 = 220

Answer 2

Jason wants to form a team of 9 players out of total 12 players.

Here the order of selection does not matter because there is no particular post for any player. So we need to use Combinations and choose 9 players out of 12 players.

We know the formula for Combinations is given as follows :-

`nCr=(n!)/(r!*(n-r)!) \\\\ Choosing \;9 \;out \;of \;12 \\\\ 12C9 = (12!)/(9!*(12-9)!) =(12!)/(9!*3!) =(12*11*10*9*8*7*6*5*4*3*2*1)/((9*8*7*6*5*4*3*2*1)*(3*2*1)) \\\\ 12C9 = (12*11*10)/(3*2*1) =(1320)/(6) =220 \;combinations`

Hence, all the possible number of different teams = 220 combinations.