GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 12 Jul 2020, 12:25 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If four numbers are randomly selected without replacement from set {1,

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 65194
If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 81% (00:53) correct 19% (00:48) wrong based on 171 sessions

### HideShow timer Statistics

If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

Kudos for a correct solution.

_________________
Senior Manager  Joined: 07 Aug 2011
Posts: 488
GMAT 1: 630 Q49 V27
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

Bunuel wrote:
If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

Kudos for a correct solution.

there is only one way to select in ascending order . 1,2,3,4

$$\frac{1}{4} *\frac{1}{3} * \frac{1}{2} = \frac{1}{24}$$

Math Expert V
Joined: 02 Aug 2009
Posts: 8757
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

3
1
Bunuel wrote:
If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

Kudos for a correct solution.

total ways to arrange four numbers = 4*3*2*1=4!=24
ways to arrange four numbers in ascending order= 1 way only..
prob = 1/24.. ans D
_________________
Senior Manager  Joined: 02 Mar 2012
Posts: 258
Schools: Schulich '16
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

1

total number of cases for selecting four numbers=4*3*2*1

case for ascending order=1(1,2,3,4)

req prob =1/4!
=1/24
Math Expert V
Joined: 02 Sep 2009
Posts: 65194
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

1
Bunuel wrote:
If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment: ascendingorder.png [ 18.99 KiB | Viewed 10890 times ]

_________________
Manager  Joined: 18 Dec 2014
Posts: 99
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

4 out of 1,2,3,4; chance = 1/4
3 out of 1,2,3; chance = 1/3
2 out of 1,2; chance = 1/2
1 out of 1; chance = 1

1/4 * 1/3 * 1/2 * 1
1*1*1*1 = 1
4*3*2*1 = 24

1/24.

D.
SVP  B
Joined: 06 Nov 2014
Posts: 1856
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

Bunuel wrote:
If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

Kudos for a correct solution.

1st number (i.e. 1) can be selected out of 4 numbers in 4 ways.
2nd number (i.e. 2) can be selected out of 3 numbers in 3 ways.
3rd number (i.e. 3) can be selected out of 2 numbers in 2 ways.
4th number (i.e. 4) can be selected out of 1 numbers in 1 ways.
Total number of ways = 4*3*2*1 = 24 ways.
Hence probability = 1/24

Hence option (D).

--
Optimus Prep's GMAT On Demand course for only \$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
Manager  B
Joined: 18 Jun 2017
Posts: 58
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

At a time we select one number.
Total outcomes =4*3*2*1=24 [since items taken out are without replacement].
So probability they are in ascending order will always be 1/24.
Option D.
Retired Moderator V
Joined: 23 Sep 2015
Posts: 1670
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

If we pick all four numbers in ascending order, that means that we select number 1 first and then number 2 second and then number 3 third and then number 4 last. So we need to calculate the individual probabilities of these events (taking into account the fact that there is NO replacement between selections), and then multiply them all together. For example, for the probability of selecting the 1 first, there's a 1 in 4 chance of selecting a 1 on the first draw. That 1 is then removed from the pool of numbers, leaving {2, 3, 4}. There is now a 1 in 3 chance of selecting the 2 from those three numbers. And so on.

Here is the math:

P(all four numbers in ascending order) =
P(1first AND 2second AND 3third AND 4fourth) =
P(1first) * P(2second) * P(3third) * P(4fourth) =
1/4 * 1/3 * 1/2 * 1 =
1/24
_________________
Simple strategy:
“Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.”

GMAT Ninja YouTube! Series 1| GMAT Ninja YouTube! Series 2 | How to Improve GMAT Quant from Q49 to a Perfect Q51 | Time management

My Notes:
Reading comprehension | Critical Reasoning | Absolute Phrases | Subjunctive Mood
Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2799
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

Bunuel wrote:
If four numbers are randomly selected without replacement from set {1, 2, 3, 4}, what is the probability that the four numbers are selected in ascending order?

A. 1/256
B. 1/64
C. 1/48
D. 1/24
E. 1/12

There are 4! = 24 arrangements of the numbers 1, 2, 3, 4. Only one arrangement is in ascending order: 1, 2, 3, 4. Therefore, the probability is 1/24.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com

214 REVIEWS

5-STARS RATED ONLINE GMAT QUANT SELF STUDY COURSE

NOW WITH GMAT VERBAL (BETA)

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

Non-Human User Joined: 09 Sep 2013
Posts: 15429
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If four numbers are randomly selected without replacement from set {1,   [#permalink] 28 May 2020, 18:18

# If four numbers are randomly selected without replacement from set {1,  