# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #2 : Factorials

Evaluate:

Explanation:

Step 1: We need to define factorial (!). The operation (!) means that you multiply the number next to the ! by the next consecutive number down to 1.

Step 2: Expand the equation:

Step 3: Evaluate the expression:

The answer to the expression is .

### Example Question #1 : Factorials

Explanation:

is the product of consecutive numbers 1 through

### Example Question #1 : Factorials

Explanation:

is the product of consecutive numbers 1 through

### Example Question #1 : Factorials

Evaluate:

Explanation:

Step 1: Rewrite the equation by using rule of factorials...

Rule of factorials: Multiply the number in front of factorial and each number one lower than the rest until I hit .

Step 2: Reduce any common numbers (colored in blue):

We get !

Step 3: Evaluate what's left

The value of the fraction is .

### Example Question #2 : Factorials

What is  equal to?

Explanation:

depicts the permutation of n total objects with k objects being arranged.

Thus,

The upper factorial is the upper index, and the lower factorial is the difference of the indices.

The  or  will cancel out.

### Example Question #7 : Factorials

Twelve horses run a race. In how many ways can 3 horses finish in 1st, 2nd, and 3rd place, in any order?

Explanation:

This particular question is asking one to find the combination. This is because the order of the 1st, 2nd, and 3rd place finishers is not important.

Thus evaluate .

Because  and  both consist of , the  will cancel out leaving:

### Example Question #1 : Factorials

Evaluate:

Explanation:

Step 1: Evaluate

Step 2: Evaluate

Step 3: Evaluate

Step 4: Evaluate

### Example Question #9 : Factorials

Evaluate:

Explanation:

Step 1: Do the division of the factorials

Step 2: Simplify by cancelling out any terms on both top and bottom:

Step 3: Multiply the result of the division by 3..

The value of that expression is .

### Example Question #1 : Factorials

Evaluate:

Explanation:

Step 1: Find

Step 2: Find

Step 3: Subtract the values from step 1 and step 2:

Evaluate: