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

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Math Expert
Joined: 02 Sep 2009
Posts: 44351
If four numbers are randomly selected without replacement from set {1, [#permalink]

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26 Mar 2015, 04:19
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Question Stats:

78% (00:29) correct 22% (00:45) wrong based on 164 sessions

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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.
[Reveal] Spoiler: OA

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Joined: 07 Aug 2011
Posts: 577
GMAT 1: 630 Q49 V27
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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26 Mar 2015, 05:02
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

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

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Math Expert
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Posts: 5723
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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26 Mar 2015, 05:29
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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
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Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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26 Mar 2015, 07:22
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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
Joined: 02 Sep 2009
Posts: 44351
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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30 Mar 2015, 03:40
1
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Expert's post
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 4255 times ]

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Joined: 18 Dec 2014
Posts: 100
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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30 Mar 2015, 09:35
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.
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Joined: 06 Nov 2014
Posts: 1902
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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31 Mar 2015, 05:18
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).

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Manager
Joined: 18 Jun 2017
Posts: 60
Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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03 Aug 2017, 03:26
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.
Re: If four numbers are randomly selected without replacement from set {1,   [#permalink] 03 Aug 2017, 03:26
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# If four numbers are randomly selected without replacement from set {1,

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