There are many techniques that you can use to help you better understand a data set. The simplest of these are the concepts of mean and average. However, that's just the beginning. On the GRE revised General Test, you can expect to see many types of math questions, some of which will require you to rely on counting methods that are more advanced than just the mean or average. Several of the counting methods that appear on the GRE exam are presented in this section.

The concept of multiplication is one of the more simplest math counting methods that you can expect to see on the GRE revised General Test. The Multiplication Principle can be stated as following:

The Multiplication Principle applies as long as the choice of one thing is independent of the choice of the other thing. If, for example, the owner of the ice cream parlor refuses to serve chocolate ice cream with chocolate syrup, then Clarisse is out of luck. The number of pairs of choices would be reduced to 5 and the Multiplication Principle would no longer apply.

The Multiplication Principle applies also when there are many choices of many things, as long as they are all independent. So, if Joe has 5 shirts, 7 pants, 4 jackets and 6 pairs of shoes (and every choice is allowed), his total number of outfits would be

The Multiplication Principle can be applied to probability experiments where there are two possible outcomes at each trial and the trials are independent. For example if a coin is tossed seven times, then there are two possible outcomes (Heads or Tails) at each trial. The total number of possible outcomes is:

For the set of Natural numbers {1, 2, 3, 4, 5, ...}, the factorial of n, if n is a natural number, is defined to be the product of all the natural numbers less than or equal to n, and is denoted by n!

For example:

Factorials are used in the calculation of Permutations and Combinations.

The concept of permutations and combinations is concerned with counting and forming subsets from a larger set. The simpler permutation and counting questions on the GRE revised General Test can be answered with pen and pencil, and by enumerating all possible combinations. But the more difficult questions will require you to know and use a few standard formula. For example, considering the following question:

Let’s label the tracks A, B, C, D, E, F, G and H. The first track you choose could be A, B, C, D, E, F, G or H, so there are 8 choices. The second track you choose could be any one of the seven remaining tracks, so there are 7 choices to choose the second track. The third track you choose could be any one of the six remaining tracks, so there are 6 choices for the third track. So, applying the Multiplication Principle, altogether for this example, you have:

We say there are 336 arrangements, or Permutations, of 3 objects chosen from 8. But are all of these choices different? That depends, and that is where some of the more difficult GRE math questions about permutations come in.

Suppose on Monday you choose track A first, followed by track B, followed by track C (ABC) then on Tuesday you choose track B first, followed by track A, followed by track C (BAC). Are these different or the same? Is ABC the same as BAC?

It depends. If A, B and C are your three absolute favorites, then it probably doesn’t matter which order you play them in. The choice is the same, but the order is different. However, if you like playing track A while you’re brushing your hair, track B while you’re cleaning your teeth and track C while you’re putting on your shoes, then order might matter. But probably you don’t really care about the order as long as you get to play your three favorites. If order doesn’t matter, then the six orderings are:

All these give you the same listening experience, so the number of choices is 336 ÷ 6 = 56.

We say there are 56 choices, or Combinations, of 3 objects chosen from 8. So, for Combinations order doesn't matter but for Permutations it does. The two important ideas:

• Combinations give the number of choices without regard to order.
• Permutations give the number of arrangements.

If you want to select k objects (or arrangements) from n choices, then the number of permutations is given by the following formula:

And the number of combinations is:

Another way to denote permutations is by

And, the number of combinations can be written as:

In all these formula, n is the number of choices, and k is how many of the choices are selected. When confronted with a counting or permutation question, you have to decide if order matters. If order matters, then use the formula for permutations, else use the formula for combinations. Below are two examples.

If the order does matter: