


Tackling What the #!*@?
Permutation and combination items are the testmakers’
lastditch effort to bring down your score. The testtakers’ 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 threestep
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.
Step 1: Does order matter? If YES, go to step 2 ONLY.
If NO, go to steps 2 and 3.
Step 2: Multiply the factorial of the number of things
being arranged to the number of spaces designated for arrangement.
Step 3: Divide by the factorial of the number of spaces
in the group.
What the #!*@? in Slow Motion
Now let’s look at the steps more closely, starting with
a fairly common What the #!*@? item.

Step 1: Does order matter? If YES, go to step 2 ONLY.
If NO, go to steps 2 and 3.
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.
Step 2: Multiply the factorial of the number of things
being arranged to the number of spaces designated for arrangement.
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.
Step 3: Divide by the factorial of the number of spaces
in the group.
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.
Guided Practice
Try this one on your own.

Step 1: Does order matter? If YES, go to step 2 ONLY.
If NO, go to steps 2 and 3.
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.
Step 2: Multiply the factorial of the number of things
being arranged to the number of spaces designated for arrangement.
Remember your factorials. Find the number of spaces in
the arrangement or group.
Step 3: Divide by the factorial of the number of spaces
in the group.
How many people or things are in the group? That is the
number you’ll use to create a factorial.
Guided Practice: Explanation
Step 1: Does order matter? If YES, go to step 2 ONLY.
If NO, go to steps 2 and 3.
The item is asking for arrangements, from left to right.
This means that order does matter. Now we go to step 2 only.
Step 2: Multiply the factorial of the number of things
being arranged to the number of spaces designated for arrangement.
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.
Step 3: Divide by the factorial of the number of spaces
in the group.
This step isn’t necessary for this item, so move on.
Independent Practice
The explanation for this item is on the following page.

Independent Practice: Explanation
Step 1: Does order matter? If YES, go to step 2 ONLY.
If NO, go to steps 2 and 3.
The key word in this item is groups,
which tells us that order does not matter. On to steps 2 and 3.
Step 2: Multiply the factorial of the number of things
being arranged to the number of spaces designated for arrangement.
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:
Step 3: Divide by the factorial of the number of spaces
in the group.
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.
