How to solve SAT Math Counting problems easily?

Remember, there are three types of SAT Math Counting Problems or questions that you might see on the SAT.

Simple Math Counting Problems
Math Counting problems where order is significant (permutation)
Math Counting problems where order is NOT significant (combination)

1. Simple Math Counting Problems

Type (1) of simple SAT Math Counting Problems asks you number of outcomes possible for different choices in given situation. In such Math Counting Problems you are given two categories and you have to make combinations by chosing one item from each category. In such situation just multiply number of items of one category with that of other category.

Remember: When determining the number of outcomes possible when combining one out of x choices in one category and one out of y choices in a second category, simply multiply x × y.

2. Math Counting problems where order is significant (permutation)

Type (2) of SAT Math Counting Problems ask you to arrange n items into r number of groups. In such Math Counting Problems order of combination is significant. It means that combination with every order will be included in counting. For example, you are asked to arrange 4 items of ABCD into groups of 2. Here, AB and BA both combinations will be included while counting number of arrangements. This type of counting is also known as Permutation. To solve these SAT Math Counting Problems specific Permutation formula is used.

Example

In how many ways the letters ABCD may be arranged in groups of two letters?

Solution.

Let’s use the formula to answer the problem of arranging the letters ABCD in groups of two letters.

the number of items (n) = 4
number of items in each permutation (r) = 2
Plug in the values into the formula:

So there are 12 possible arrangements for combining 4 letters ABCD into group of two.

AB AC AD BA BC BD
CA CB CD DA DB DC

3. Math Counting problems where order is NOT significant (combination)

These types of SAT Math Counting Problems ask you to arrange n number of items in r groups. In these Math Counting Problems order of arrangement is not significant. It means you have to exclude repetitive arrangements with opposite order. For example, if you are arranging ABCD into group of two, you’ll see AB, BA or BC, CB etc. in the arrangement. You’ll have to count only one out of these two. You’ll count them as two not four. This is also called combination.You may use following Math Combination formula for solving such SAT Math Counting Problems.

Example

To determine the number of three-letter combinations from a group of seven letters (ABCDEFGH), use the following values: n = 7 and r = 3.

Substitute the values into the formula:

Therefore, there are 35 three-letter combinations from a group of seven letters.

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