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GRE Subject Test: Math : Permutations

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Example Question #91 : Probability & Statistics

How many three-digit numbers can I create from the set of numbers $\{2,2,4,5,6,7,9\}$ ?

Possible Answers:

343

210

294

252

Correct answer:

343

Explanation:

Step 1: Identify if there are any restrictions to how the numbers can be made...

There are no restrictions, so we can have repeating numbers.

Step 2: Determine how many numbers can go in each slot..

First Slot: 7 choices
Second Slot: 7 Choices
Third Slot: 7 choices

Step 3: Multiply the choices for all three sets together:

$7\cdot7\cdot7\equiv7^3\equiv 343$

We can create 343 different three-digit numbers...

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Example Question #91 : Probability & Statistics

How many non-repetitive three-digit numbers can I create from the set of numbers $\{1,2,3,4,5,6,7,9\}$ ?

Possible Answers:

336

307

350

376

Correct answer:

336

Explanation:

Step 1: See if there are any restrictions..

We see we want only non-repetitive numbers...

Step 2: Find how many numbers can be put in each spot:

First Spot:
Second Spot:
Third Spot:

Step 3: Multiply the number of choices of each spot

$8\cdot6\cdot7=336$

I can create 336 non-repetitive three-digit numbers...

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Example Question #91 : Other Topics

How many ways can I arrange the letters in the word MISSISSIPPI ?

Possible Answers:

34650

34800

35353

34500

Correct answer:

34650

Explanation:

Step 1: Count how many letters are in the word MISSISSIPPI...

There are 11 numbers.

Step 2: Find which letters repeat, and how many times it repeats:

I-4 times
S-4 times
P-2 times

Step 3: Use formula for arranging letters:

$\frac {(Total\\Letters)!}{(Repeats)!}=\frac {11!}{2!4!4!}$

Step 4: Expand:

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

Step 5: Simplify Step 4:

$\frac {11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5}{4}=11\cdot10\cdot9\cdot2\cdot7\cdot6\cdot5=34650$

I can rearrange the letters in MISSISSIPPI 34650 times...

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Example Question #591 : Gre Subject Test: Math

How many ways can I arrange the letters in the word CORRECT?

Possible Answers:

$1260$

$1080$

$900$

$720$

Correct answer:

$1260$

Explanation:

Step 1: Count how many letters are in the word CORRECT...

There are letters.

Step 2: Find any letters that repeat and how many times they repeat:

C (two times), R (two times)

Step 3: Find how many ways can I arrange the letters:

$\frac{7!}{2!2!}=\frac {7*6*5*4*3*2*1}{2*1*2*1}=7*6*5*3*2=1260$

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Example Question #101 : Other Topics

people are at a farewell party. At the end of the night, each person shakes hands. How many handshakes are made?

NOTE: No two people can shake hands more than once.

Possible Answers:

Correct answer:

Explanation:

Step 1: Determine how many people are there..
There are people.
Step 2: Determine how many people shake hands in a handshake...
people make one handshake.
Step 3: Determine how many handshakes can be made...
We have a restriction here, so we need to use permutation..

So, there will be 11P2 handshakes.

$11P2=\frac {11*10}{2*1}=11*5=55$ handshakes

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Example Question #51 : Combinational Analysis

In how many ways can I rearrange the letters in the word "ANACONDA"?

Possible Answers:

3360

4000

3830

3000

Correct answer:

3360

Explanation:

Step 1: Count how many letters are in the word ANACONDA...

There are 8 letters.

Step 2: Count how many repeats of any letters (if any)..

There are A's and N's.

Step 3: Find how many ways I can rearrange...

$\frac {8!}{3!*2!}=\frac {8*7*6*5*4*3*2*1}{3*2*1*2*1}...$

$...=\frac {8*7*6*5*4}{2}=8*7*6*5*2=3360$

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Example Question #11 : Permutations

How many ways can I arrange the letters in the word TRIGONOMETRY ?

Possible Answers:

$\frac {12!}{2!\times2!\times2!}$

${2!\times2!\times2!}$

$\frac {12!}{2!\times2!\times3!}$

{12!}

Correct answer:

$\frac {12!}{2!\times2!\times2!}$

Explanation:

Step 1: Count how many numbers are in the word...

There are letters.

Step 2: Count the number of repeated letters...

There are T's

There are O's

There are R's

Step 3: To find how many ways I can arrange the letters, take the factorial of the total number of letters and divide it by the factorial of how many times a certain letter repeats...

So, $\frac {12!}{2!\times2!\times2!}$

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GRE Subject Test: Math : Permutations

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #91 : Probability & Statistics

Example Question #91 : Probability & Statistics

Example Question #91 : Other Topics

Example Question #591 : Gre Subject Test: Math

Example Question #101 : Other Topics

Example Question #51 : Combinational Analysis

Example Question #11 : Permutations

All GRE Subject Test: Math Resources

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