Even though there exist many methods through which students can get a better understanding of a data set, of which mean and median are the simplest technique of all. But when it comes to GRE, it tests students through different mathematical problems. And these problems need more sophisticated methods; such as counting methods for solving than compared to the simple average techniques used. This article presents several of the counting methods that are listed on the GRE syllabus.

**The Principle of Multiplication**

The concept lying in the roots of the principle of multiplication can be considered to be the simplest counting methods that you can presume of witnessing in the GRE revised General Test. The Principle of Multiplication can be stated as follows:

Suppose, if there are l choices for one article and k options for another item, then the likely unique possibilities for the pair of articles will be l ×k or lk.

**Also Read: **Exponents & Roots

The Principle of Multiplication is applicable only if the choices of one thing with respect to the other are entirely independent. This principle will also apply if there are many alternatives of many articles, as long as they are independent of one another. For example; If Monica has 8 shirts, 5 skirts, 7 jeans, 3 jackets and 9 pairs of shoes then the total number of outfits she has equals to 8 × 5 × 7 × 3 × 9 = 7560

The Multiplication Principle can also be applied to the probabilistic situations where the possible outcomes are always two at each trial, and the trials are independent of one another. For example, if a coin is being tossed five times. In this case, there are only two possible outcomes (either heads or tails) in each trial.

Hence, total number of possible outcomes = 2 × 2 × 2 × 2 × 2 = 25 = 32

**Factorials:**

For a set of Natural numbers {1, 2, 3, 4, 5, …}, the factorial of n can be represented as n!, where n is a natural number, and it is defined as the product of all the natural numbers that are less than and equal to n.

For example; 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Factorials are mainly used for permutation and combination.

**Also Read: **Operations with Algebraic Expression

**Permutation & Combination**

Permutation: An ordered arrangement of objects is known as a permutation. The formula used for calculating permutations for r objects taken from n different objects is:

\(\large ^{n}P_{r} = \frac{n!}{(n -r)!}\)

Combination: Ways of selecting items from a group, in which the order of selection does not matter. The formula used for calculating combination is:

\(\large ^{n}C_{r} = \frac{^{n}P_{r}}{r!} = \frac{n!}{r!(n -r)!}\)