Question 1193874: A coach must reduce his basketball team from 13 players to 11 players.
Among how many different final teams has he to choose?
13C11= 13C2
= 13 x 12/2!
= 156/2
= 78
What is the probability that a particular player, S, will be chosen to remain on the team?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Let's say we want player S a guaranteed spot on the team.
That leaves n = 13-1 = 12 players left to pick from and r = 11-1 = 10 slots to fill.
nCr = (n!)/(r!*(n-r)!)
12C10 = (12!)/(10!*(12-10)!)
12C10 = (12!)/(10!*2!)
12C10 = (12*11*10!)/(10!*2!)
12C10 = (12*11)/(2!)
12C10 = (12*11)/(2*1)
12C10 = 132/2
12C10 = 66
There are 66 ways to form a team where we guarantee that player S is on the team.
As you calculated correctly, 13C11 = 78 is the number of ways to select 11 players from a pool of 13.
Among these 78 total cases, player S may or may not be on the team.
The probability player S is on the team is 66/78 = (6*11)/(6*13) = 11/13
We divide the number of ways to form a team with player S on it (66) over the number of teams total (78).
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