Permutation and combination items are the test-makers’ last-ditch effort to bring down your score. The test-takers’ usual reaction to these items is “What the #!*@?” Believe it or not, this visceral reaction can actually help you identify a permutation or combination item. When you find yourself frustrated beyond belief, there is a very good chance you’re looking at one of these items.

Once you’ve collected yourself, follow the three-step method below for solving What the #!*@? items. Not only will it lead you to the correct answer but to a new found feeling of empowerment from shredding the SAT math section.

Now let’s look at the steps more closely, starting with a fairly common What the #!*@? item.

Susanne is placing two medals onto a mounted frame. Does it matter in which order the medals are placed? No, the word combinations in the item tells us that order does not matter. Recall from our study of the essential concepts that combinations deal with groups of things, while permutations deal with arrangements. In permutations, order matters.

Now let’s move on and complete steps 2 and 3.

This step is actually easier than it sounds. How many medals does Susanne have to arrange? 11. How many spaces on her frame does she have for arrangement? 2. So all we do is multiply the first two values in the factorial of 11 (11!):

Susanne has 11 medals to choose from for the first space and 10 to choose from for the second space.

Because there are two positions on the frame, we go ahead and divide by the factorial of 2, (2!). So now our entire equation looks like this: . That’s it, that’s all! The correct answer is C, 55.

Try this one on your own.

Is the item asking about groups or arrangements? If it is a group, then order does not matter. If it is not a group, then it must be an arrangement, and order does matter.

Remember your factorials. Find the number of spaces in the arrangement or group.

How many people or things are in the group? That is the number you’ll use to create a factorial.

The item is asking for arrangements, from left to right. This means that order does matter. Now we go to step 2 only.

How many things are being arranged? Six spices. How many spaces on the spice rack are there for them? Four. Now multiply the factorial of the number of spices (6!) down to the number of spaces available. It should look like this:

That’s the number of arrangements, answer E. I hope Kevin doesn’t ask us to help.

This step isn’t necessary for this item, so move on.

The explanation for this item is on the following page.

The key word in this item is groups, which tells us that order does not matter. On to steps 2 and 3.

How many people or things are being arranged? Nine freshmen. How many spaces are there on the student council for them? Five. The factorial of 9, (9!), multiplied down five spaces looks like this:

How many freshmen are going to be in the group? Five. So we are going to divide by the factorial of 5, (5!). Here’s our entire equation:

That’s it! There is the possibility of 126 groups of 5 freshmen to fill the vacancies of the student council. Our answer is choice C, 126.