Unless you live in France, you’ve likely been excited about World Cup action the past two weeks. With upsets galore — including both previous finalists, France and Italy, knocked out in the opening round — and intense drama — perhaps most incredible was Landon Donovan’s 91st minute goal to propel the United States to the elimination round — the 2010 World Cup has demonstrated why it’s widely considered the world’s most beloved sporting event.

Like many fans, you may even be playing in a fantasy league or participating in a bracket contest (with the American daytime game times, the World Cup does feel quite a bit like March Madness). If you’re playing in the ESPN.com bracket challenge, you may have noticed an interesting, GMAT-related trend in the way that the first round has been scored:

Order matters.

In the Veritas Prep company bracket tournament, several members of the group correctly selected the United States and England to advance to the elimination round. However, those who unpatriotically picked England to win the group and the U.S. to finish second were in for a rude awakening when looking at the rest of the tournament; not only did they lose points for not having the correct order for the first round, they also have the elimination round brackets set up incorrectly and will lose future points for not having the winners in the correct games. If the order of the first round was not correct, correctly picking England to win its first elimination game will still be an “incorrect” pick, because they’re not playing in the same game as the one on your bracket.

While frustrating for the Benedict Arnolds of the world who picked England to finish first in the group, it also provides a helpful GMAT lesson: know when the order matters!

When you deal with permutations and combinations problems on the GMAT, you’ll use two different formulas depending on whether the question asks for a permutation (order matters) or combination (order does not matter):

N = Number of items, total
K = Number of items to be selected from the group of N

Permutation:

N!/(N-K)!

Combination:

N!/(K!(N-K)!)

Essentially, because there are K! ways to arrange each group of K items in order, multiplying the number of combinations by K! will provide the number of orders.

Even if you simply memorize those formulas (not a bad idea, actually), you must be able to identify when to use each. Remember, permutations are when the order matters, and combinations are when it doesn’t. Examples include:

Of a group of 15 students, how many 9-player baseball teams could be created?

Combination — the order does not matter.

Of a group of 15 students, how many 9-player batting orders could be created?

Permutation — the order does matter.

How many ways can 8 flags be displayed in a row?

Permutation — the order does matter.

From a group of 9 students, how many 4-person project teams can be created?

Combination — order does not matter.

Much like in the ESPN World Cup bracket pool, much of your success on combinatorics questions will be determined by whether you can determine when the order matters. Make this a primary decision point when setting up questions, and you’ll be that much closer to accomplishing your GMAT gooooooooooooaaaaaaaaaal!!!!!!

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