# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #1 : Permutations

Abby, Bryan, Cindy, Doug, and Ernie are sitting on a bench. How many ways can I arrange their seating order?

Explanation:

Step 1: We need to identify how many seats there are on the bench. We have 5 names, so 5 seats.

Step 2: When 1 person sits in seat 1, he/she cannot sit in the next set, and so on.

Step 3: Let's work out the math...

Seat 1- 5 people can sit
Seat 2- 4 people can sit
Seat 3- 3 people can sit
Seat 4/5-2/1 people/person can sit

Total possibilities=. We can also say that

### Example Question #4 : Permutations

There are 12 boys in a football competition,  the top 3 competitors are awarded with an trophy. How may possible groups of 3 are there for this competition?

Explanation:

This is a permutation. A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as

There are  possible groups of 3.

### Example Question #1 : Permutations

An ice cream shop has 23 flavors. Melissa wants to buy a 3-scoop cone with 3 different flavors, How many cones can she buy if order is important?

Explanation:

This is a permutation. A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as

represents the number of permutations of 23 things taken 3 at a time.

### Example Question #4 : Permutations

Find the value of  .

Explanation:

is asking to find the permutation of seven items when you want to choose five. When dealing with permutations, order matters.

A permutation is an arrangement of objects in a specific order.

The formula for permutations is:

This is written as

### Example Question #5 : Permutations

Evaluate .

Explanation:

is asking to find the permutation of four items when you want to choose all four. When dealing with permutations, order matters.

A permutation is an arrangement of objects in a specific order.

The formula for permutations in this case will be,

or  factorial.

### Example Question #6 : Permutations

There are  people at a family dinner. After the dinner is over, people shake hands with each other. How many handshakes were there between these  people. Note: Once two people shake hands, they cannot shake hands again..

Explanation:

Step 1: A handshake MUST ALWAYS be between TWO people.

Step 2: Break down each person and who they can shake hands with:

Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:
Person  can shake hands with:

Step 3: Count how many handshakes each person can make:

Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  times.
Person  shakes hands  time.

Step 4: Add up the number of times each person shook hands:

There were  handshakes made between these  people.

### Example Question #11 : Permutations

How many three-digit numbers can I create from the set of numbers ?

Explanation:

Step 1: Identify if there are any restrictions to how the numbers can be made...

There are no restrictions, so we can have repeating numbers.

Step 2: Determine how many numbers can go in each slot..

First Slot: 7 choices
Second Slot: 7 Choices
Third Slot: 7 choices

Step 3: Multiply the choices for all three sets together:

We can create  different three-digit numbers...

### Example Question #91 : Probability & Statistics

How many non-repetitive three-digit numbers can I create from the set of numbers ?

Explanation:

Step 1: See if there are any restrictions..

We see we want only non-repetitive numbers...

Step 2: Find how many numbers can be put in each spot:

First Spot:
Second Spot:
Third Spot:

Step 3: Multiply the number of choices of each spot

I can create  non-repetitive three-digit numbers...

### Example Question #92 : Probability & Statistics

How many ways can I arrange the letters in the word ?

Explanation:

Step 1: Count how many letters are in the word MISSISSIPPI...

There are 11 numbers.

Step 2: Find which letters repeat, and how many times it repeats:

times
times
times

Step 3: Use formula for arranging letters:

Step 4: Expand:

Step 5: Simplify Step 4:

I can rearrange the letters in MISSISSIPPI  times...

### Example Question #14 : Permutations

How many ways can I arrange the letters in the word CORRECT?

Explanation:

Step 1: Count how many letters are in the word CORRECT...

There are  letters.

Step 2: Find any letters that repeat and how many times they repeat:

C (two times), R (two times)

Step 3: Find how many ways can I arrange the letters: