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by student4gmat » Mon Sep 29, 2014 9:27 am
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?
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by GMATGuruNY » Mon Sep 29, 2014 10:00 am
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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by student4gmat » Mon Sep 29, 2014 10:14 am
GMATGuruNY wrote:
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.
\


Ok I got this method...thanks.

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.
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by GMATGuruNY » Mon Sep 29, 2014 10:27 am
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.
You have correctly counted how many 11-member teams can be formed if Rahul or Sachin is included:
2C1 * 14C10 = 2C1 * 14C4 = 2 * (14*13*12*11)/(4*3*2*1) = 2002.

Now we must count how many 11-member teams can be formed if neither Rahul nor Sachin is included.
From the 14 other players, the number of ways to choose 11 = 14C11 = 14C3 = (14*13*12)/(3*2*1) = 364.

Thus:
Total possible teams = 2002 + 364 = 2366.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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