Question 1193874
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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) = <font color=red>11/13</font>
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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