All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Factorials
Simplify the following expression:
Recall that ! means facotrial 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 : Factorials
Evaluate:Â
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 #2 : Combinational Analysis
 is the product of consecutive numbers 1 throughÂ
Â
Example Question #2 : Factorials
 is the product of consecutive numbers 1 throughÂ
Â
Example Question #2 : Factorials
Evaluate:Â Â
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 #3 : Factorials
What is  equal to?
 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.Â
Â
The  orÂ
 will cancel out.
Example Question #52 : Probability & Statistics
Twelve horses run a race. In how many ways can 3 horses finish in 1st, 2nd, and 3rd place, in any order?
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 .
Â
Because  andÂ
 both consist ofÂ
, theÂ
 will cancel out leaving:
Â
Â
Example Question #1 : Combinational Analysis
Evaluate:Â
Step 1: EvaluateÂ
Step 2: EvaluateÂ
Step 3: EvaluateÂ
Step 4: EvaluateÂ
Step 5: Add/Subtract values:
Example Question #3 : Combinational Analysis
Evaluate:Â Â
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 #10 : Factorials
Evaluate:Â
Step 1: FindÂ
Step 2: FindÂ
Step 3: Subtract the values from step 1 and step 2:
The answer isÂ
Â
Â
All GRE Subject Test: Math Resources
