McGraw-Hill Education GRE 2019

Permutations

One application of the fundamental counting principle concerns questions that

ask you for the number of ways the items in a set can be ordered. These are called

permutation questions and usually use the words orderings or arrangements. To

answer such questions, you should use the slot method. Let’s use the following

example to illustrate how the slot method works:

For this question, write your answer in the box.

How many five-digit locker codes can be created from the digits 0–9,

inclusive, if no digit can repeat?

SOLUTION: The order of the digits is relevant to the question, so consider it a

permutation and use the slot method.

Step 1: Set up a number of slots corresponding to the number of items that

are being selected. Since the code is five digits, you will set up five slots:

Step 2: Starting with the first slot, put in the number of possible choices

for each slot. Since you are selecting from 10 digits, there are 10 possibilities

for the first slot. Since the digits cannot repeat, whichever number occupies

the first slot cannot occupy the second slot. Thus there are 9 possibilities for

the second slot. By the same reasoning, there are 8 possibilities for the third

slot, 7 possibilities for the fourth slot, and 6 possibilities for the fifth slot.

The slots should thus look like the following:

10 9 8 7 6

Step 3: Multiply across.

10 × 9 × 8 × 7 × 6 = 30,240

358 PART 4 ■ MATH REVIEW

04-GRE-Test-2018_313-462.indd 358 12/05/17 12:04 pm