GRE Subject Test: Math : Factorials

Study concepts, example questions & explanations for GRE Subject Test: Math

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1

Example Question #50 : Other Topics

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

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: 

Possible Answers:

Correct answer:

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 #2 : Factorials

Possible Answers:

Correct answer:

Explanation:

 is the product of consecutive numbers 1 through 

 

Example Question #3 : Factorials

Possible Answers:

Correct answer:

Explanation:

 is the product of consecutive numbers 1 through 

 

Example Question #4 : Factorials

Evaluate:  

Possible Answers:

Correct answer:

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 #5 : Factorials

What is  equal to?

Possible Answers:

Correct answer:

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 #6 : Factorials

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

Possible Answers:

Correct answer:

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 #7 : Factorials

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Evaluate 



Step 2: Evaluate 



Step 3: Evaluate 



Step 4: Evaluate 



Step 5: Add/Subtract values:

Example Question #8 : Factorials

Evaluate:  

Possible Answers:

Correct answer:

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 #9 : Factorials

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Step 1: Find 



Step 2: Find 



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



The answer is 

 

 

← Previous 1
Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: