# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #81 : Probability & Statistics

Find .

Explanation:

There are two types of statistical calculations that are used when dealing with ordering a number of objects. When the order does not matter it is known as a combination and denoted by a C.

Thus the formula for this particular combination is,

### Example Question #13 : Combinations

Six points are located on a circle. How many line segments can be drawn?

Explanation:

There are two types of statistical calculations that are used when dealing with ordering a number of objects. When the order does not matter it is known as a combination and denoted by a C.

Thus the formula for this particular combination is,

There are 2 points on each line segment.

### Example Question #82 : Probability & Statistics

Evaluate .

Explanation:

Evaluate  is asking to calculate the combination of five objects when choosing three of them.

or  cancels out.

### Example Question #83 : Probability & Statistics

How many ways can I get non-repetitive three-digit numbers from the numbers: ?

Explanation:

Step 1: Count how many numbers I can use..

I can use 9 numbers.

Step 2: Determine how many numbers I can put in the first digit of the three-digit number..

I can put  numbers in the first spot. I cannot put  in the first slot because the number will not be a three-digit number.

Step 3: Determine how many numbers I can put in the second digit..

I can also put  numbers in the second spot. Here's the reason why it's still :

Let's say I choose 2 for the first number. I will take  out of my set. I had numbers in my set..If i take a number out, I still have  numbers left. These numbers are: .

Step 4: Determine how many numbers I can put in the third and final digit...

I can put  numbers in the third slot..

I had  numbers at the start, and then I removed  of them. .

Step 5: Multiply how many numbers can go in the first, second, and third spot..

.

There are a total of  non-repetitive three-digit numbers that can be formed.

### Example Question #581 : Gre Subject Test: Math

A coach of a baseball team needs to choose  players out of a total  players in the team. How many ways can the coach choose 9 players?

Explanation:

Step 1: Recall the combination formula...

Step 2: Find  and  from the question..

.

Step 3: Plug in the values into the formula above..

### Example Question #17 : Combinations

Six people run in a race, in how many different orders can they finish?

Explanation:

This problem is solved by knowing that we have six options for first place, five options for second place, and so on.

Which means

### Example Question #1 : 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 #2 : Permutations

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.

Quantity B is greater.

The two quantities are equal.

The relationship cannot be determined.

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 #3 : 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