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Good teams = (all possible teams) - (bad teams).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?
\GMATGuruNY wrote:Good teams = (all possible teams) - (bad teams).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?
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.
You have correctly counted how many 11-member teams can be formed if Rahul or Sachin is included:student4gmat wrote:Can you please explain if we can do it the other way...rather than finding total and subtracting what we do not want...can we only find what we want.
The question says If R is selected S will not be selected, if S is selected R will not be selected. means out of these 2 people only 1 wil be selected so
2C1 * 14C10
Is this wrong. If yes, then could you please explain what am I doing wrong.
