# GRE Subject Test: Math : Permutations

## Example Questions

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### Example Question #2 : Permutation / Combination

Daisy wants to arrange four vases in a row outside of her garden. She has eight vases to choose from. How many vase arrangements can she make?

Explanation:

For this problem, since the order of the vases matters (red blue yellow is different than blue red yellow), we're dealing with permutations.

With  selections made from  potential options, the total number of possible permutations(order matters) is:

### Example Question #31 : Permutation / Combination

Lisa is dressing warm for the winter. She'll be layering three shirts over each other, and two pairs of socks. If she has fifteen shirts to choose from, along with ten different kinds of socks, how many ways can she layer up?

Explanation:

Since the order in which Lisa layers up matters, we're dealing with permutations.

With  selections made from  potential options, the total number of possible permutations is:

For her shirts:

For her socks:

Her total ensemble options  is the product of these two results

### Example Question #32 : Permutation / Combination

Quantity A: The number of possible permutations when seven choices are made from ten options.

Quantity B: The number of possible permutations when five choices are made from eleven options.

The relationship cannot be determined.

Quantity B is greater.

The two quantities are equal.

Quantity A is greater.

Quantity A is greater.

Explanation:

With  selections made from  potential options, the total number of possible permutations(order matters) is:

Quantity A:

Quantity B:

Quantity A is greater.

### Example Question #1 : Permutations

Jill is picking out outfits for a three-day weekend, one for Friday, one for Saturday, and one for Sunday.

Fortunately all of her clothes match together really well, so she can be creative with her options, though she's decided each outfit is going to be a combination of blouse, skirt, and shoes.

She'll be picking from ten blouses, twelve skirts, and eight pairs of shoes. How many ways could her weekend ensemble be lined up?

Explanation:

For this problem, order matters! Wearing a particular blouse on Friday is not the same as wearing it on Sunday. So that means that this problem will be dealing with permutations.

With  selections made from  potential options, the total number of possible permutations(order matters) is:

What we'll do is calculate the number of permutations for her blouses, skirts, and shoes seperately (determining how the Friday/Saturday/Sunday blouses/skirts/shoes could be decided), and then multiply these values.

Blouses:

Skirts:

Shoes:

Thus the number of potential outfit assignments is

### Example Question #2 : 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 #3 : 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 #4 : 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 #5 : 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 #6 : 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 #7 : 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.

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