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GRE Subject Test: Math : Probability & Statistics

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

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All GRE Subject Test: Math Resources

2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #12 : Combinational Analysis

Evaluate: $\frac {14!}{13!}$

Possible Answers:

183

Correct answer:

Explanation:

Step 1: Expand the numerator and denominator:

$\frac {14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

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

We are left with .

The value of $\frac {14!}{13!}=14$

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Example Question #61 : Other Topics

What is ?

Possible Answers:

720

Correct answer:

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

3!=3(3-1)(3-2)(1)=3(2)(1)=6(1)=6

3!=6

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Example Question #561 : Gre Subject Test: Math

Evaluate:

Possible Answers:

3628800

120

40320

5040

Correct answer:

40320

Explanation:

Step 1: Evaluate
Factorial-Multiply the number in front of the exclamation point by every number below until I hit
8!=8*7*6*5*4*3*2*1=40320

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Example Question #562 : Gre Subject Test: Math

Evaluate: 2!*3!*4!

Possible Answers:

256

273

288

179

Correct answer:

288

Explanation:

Step 1: Evaluate each factorial expression separately...

2!=2*1=2
3!=3*2*1=6
4!=4*3*2*1=24

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

So, we get 2*6*24=288

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Example Question #563 : Gre Subject Test: Math

Evaluate: $3!^{2^{3!}}$

Possible Answers:

6^4

4^6

$6^{12}$

$6^{6^{6}}$

Correct answer:

$6^{12}$

Explanation:

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

We get $3!^{2*3!}$

Step 2: Evaluate the exponent...

We get $3!^{2*6}=3!^{12}$

Step 3: Re-write the base:

Final answer: $6^{12}$

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Example Question #564 : Gre Subject Test: Math

Evaluate: $\large 4(3!)$

Possible Answers:

$\large 6!$

12!

$\large 24$

Correct answer:

$\large 24$

Explanation:

Step 1: Evaluate the parentheses first

$\large (3!)=(3*2*1)=6$

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

$\large 6(4)=24$

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Example Question #565 : Gre Subject Test: Math

Evaluate: $\large 5!$

Possible Answers:

$\large 720$

$\large 121$

$\large 360$

$\large 120$

Correct answer:

$\large 120$

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 $\large 5!$

$\large 5!=5(5-1)(5-2)(5-3)(5-4)$
$\large 5!=5*4*3*2*1=120$

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Example Question #67 : Other Topics

Evaluate:

7!-6(6!)

Possible Answers:

None of the other answers

720

480

120

432

Correct answer:

720

Explanation:

Evaluate $\large 7!$ :

$\large 7!=7\cdot 6\cdot5\cdot4\cdot3\cdot2\cdot1=5040$

Evaluate $\large 6(6!)$ :

$\large \large 6(6!)=6(6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1)=6(720)=4320$

Evaluate $\large 7!-6(6!)$ :

$\large 5040-4320=720$

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Example Question #17 : Factorials

Simplify the following expression:

$\frac{12!}{10!-4!}$

Possible Answers:

132.0009

121

132

123.004

366

Correct answer:

132.0009

Explanation:

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

$\frac{12!}{10!-4!}$

Becomes

$\frac{1\cdot 2\cdot3\cdot 4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10\cdot11\cdot12}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10)-(1\cdot2\cdot3\cdot 4)}$

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

132.0009

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Example Question #21 : Combinational Analysis

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?

Possible Answers:

2427300

202275

40455

242730

44950

Correct answer:

40455

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:

$C(n,k)=\frac{n!}{(n-k)!k!}$

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:

$C(31,3)=\frac{31!}{(31-3)!3!}=4495$

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:

$C(9,1)=\frac{9!}{(9-1)!1!}=9$

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:

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GRE Subject Test: Math : Probability & Statistics

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #12 : Combinational Analysis

Example Question #61 : Other Topics

Example Question #561 : Gre Subject Test: Math

Example Question #562 : Gre Subject Test: Math

Example Question #563 : Gre Subject Test: Math

Example Question #564 : Gre Subject Test: Math

Example Question #565 : Gre Subject Test: Math

Example Question #67 : Other Topics

Example Question #17 : Factorials

Example Question #21 : Combinational Analysis

All GRE Subject Test: Math Resources

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