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For the most part on GMAT - you will be using the nCr formula -- like 3C2 ---out of 3 choose 2.
Out of 3 people -- choose 2 people to be a team.
Let's say you have persons A, B, and C (3 people).
Team #1 = A and B
Team #2 = A and C
Team #3 = B and C
So you can have a total possible combinations of 3 teams when you pick 2 people out of 3.
This is when order does not matter. It does not matter for Team #1 that you pick A first and then B. Or B first and then A. They are both counted as 1.
This is called combination -- this is most common.
Occasionally, you may be asked about what happens when order matters.
For example, what if each team member is chosen to run a lap around a race track? If the question asks you how many different possibilities of runner line-ups -- then the order would matter.
If person A runs first, then person B -- that is counted as a different lineup as person B running first and then person A.
So now with permutations -- the notation is technically 3P2.
You would get
Team #1 = A and B
Team #2 = A and C
Team #3 = B and C
Team #4 = B and A
Team #5 = C and A
Team #6 = C and B
Calculation-wise, you can still express this in terms of nCr.
Typically, (3C2) = (3!) / (2!) = 6 / 2 = 3
Note the dividing by (2!) -- is because we need adjust for the fact that ORDER DOES NOT MATTER in typical combination questions.
But if we are dealing with PERMUTATIONS - -then we do NOT need to divide by 2!.
It would simply be 3! = 3*2*1 = 6
So with combinations we get 3 possibilities.
With permutations we get 6 possibilities.
Out of 3 people -- choose 2 people to be a team.
Let's say you have persons A, B, and C (3 people).
Team #1 = A and B
Team #2 = A and C
Team #3 = B and C
So you can have a total possible combinations of 3 teams when you pick 2 people out of 3.
This is when order does not matter. It does not matter for Team #1 that you pick A first and then B. Or B first and then A. They are both counted as 1.
This is called combination -- this is most common.
Occasionally, you may be asked about what happens when order matters.
For example, what if each team member is chosen to run a lap around a race track? If the question asks you how many different possibilities of runner line-ups -- then the order would matter.
If person A runs first, then person B -- that is counted as a different lineup as person B running first and then person A.
So now with permutations -- the notation is technically 3P2.
You would get
Team #1 = A and B
Team #2 = A and C
Team #3 = B and C
Team #4 = B and A
Team #5 = C and A
Team #6 = C and B
Calculation-wise, you can still express this in terms of nCr.
Typically, (3C2) = (3!) / (2!) = 6 / 2 = 3
Note the dividing by (2!) -- is because we need adjust for the fact that ORDER DOES NOT MATTER in typical combination questions.
But if we are dealing with PERMUTATIONS - -then we do NOT need to divide by 2!.
It would simply be 3! = 3*2*1 = 6
So with combinations we get 3 possibilities.
With permutations we get 6 possibilities.
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