student4gmat wrote:There are total 16 players - Sachin, Rahul and 14 others. We need to select 11 players such that
If Rahul is selected, Sachin is not selected and if Sachin is selected Rahul is not selected. How many ways are possible?
Good teams = (all possible teams) - (bad teams).
A useful shortcut:
nCr = nC(n-r).
To illustrate:
5C4 = 5C(5-4) = 5C1 = 5.
All possible teams:
From 16 players, the number of ways to choose 11 = 16C11 = 16C5 = (16*15*14*13*12)/(5*4*3*2*1) = 4368.
Bad teams:
A bad team = (Rahul and Sachin) + (9 of the 14 other players).
From the 14 other players, the number of ways to choose a combination of 9 to join Rahul and Sachin = 14C9 = 14C5 = (14*13*12*11*10)/(5*4*3*2*1) = 2002.
Thus:
Good teams = 4368 -2002 =
2366.
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