# GRE Subject Test: Math : Probability & Statistics

## Example Questions

### Example Question #12 : Factorials

Evaluate:

Explanation:

Step 1: Expand the numerator and denominator:

Step 2: Cross all numbers out that are common to both the numerator and denominator:

We are left with .

The value of

### Example Question #561 : Gre Subject Test: Math

What is ?

Explanation:

Step 1: Recall definition of factorial...

Factorial is a mathematical expression where you multiply  by every number below it until I hit . To find each number, subtract  from the previous number

Step 2: Write out

### Example Question #14 : Factorials

Evaluate:

Explanation:

Step 1: Evaluate
Factorial-Multiply the number in front of the exclamation point by every number below until I hit

### Example Question #15 : Factorials

Evaluate:

Explanation:

Step 1: Evaluate each factorial expression separately...

Step 2: Take the evaluation of each expression and apply the operations in the problem:

So, we get

### Example Question #16 : Factorials

Evaluate:

Explanation:

Step 1: Apply the power rule (stacked) of exponents..

We get

Step 2: Evaluate the exponent...

We get

Step 3: Re-write the base:

### Example Question #17 : Factorials

Evaluate:

Explanation:

Step 1: Evaluate the parentheses first

Step 2: Multiply the outside by the final value in Step 1..

### Example Question #11 : Factorials

Evaluate:

Explanation:

Step 1: Define Factorial

Factorial is a mathematical expression which you multiply the number in front of the exclamation point by every number below it until you hit 1..

Step 2: Evaluate

Evaluate:

Explanation:

Evaluate :

Evaluate :

Evaluate :

### Example Question #20 : Factorials

Simplify the following expression:

Explanation:

Recall that ! means factorial in math. This means we multiply the number by all positive integers less than itself. In other words, this...

Becomes

This is a great job for a calculator, which yields:

### Example Question #1 : Combinations

Mohammed is being treated to ice cream for his birthday, and he's allowed to build a three-scoop sundae from any of the thirty-one available flavors, with the only condition being that each of these flavors be unique. He's also allowed to pick  different toppings of the available , although he's already decided well in advance that one of them is going to be peanut butter cup pieces.

Knowing these details, how many sundae combinations are available?

Explanation:

Because order is not important in this problem (i.e. chocolate chip, pecan, butterscotch is no different than pecan, butterscotch, chocolate chip), it is dealing with combinations rather than permutations.

The formula for a combination is given as:

where  is the number of options and  is the size of the combination.

For the ice cream choices, there are thirty-one options to build a three-scoop sundae. So, the number of ice cream combinations is given as:

Now, for the topping combinations, we are told there are ten options and that Mohammed is allowed to pick two items; however, we are also told that Mohammed has already chosen one, so this leaves nine options with one item being selected:

So there are 9 "combinations" (using the word a bit loosely) available for the toppings. This is perhaps intuitive, but it's worth doing the math.

Now, to find the total sundae combinations—ice cream and toppings both—we multiply these two totals: