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

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

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

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New post 26 Mar 2015, 04:02
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

\(\frac{1}{4} *\frac{1}{3} * \frac{1}{2} = \frac{1}{24}\)

Answer D.
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Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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New post 26 Mar 2015, 04:29
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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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New post 26 Mar 2015, 06:22
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Answer is D

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

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

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New post 30 Mar 2015, 02:40
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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
ascendingorder.png [ 18.99 KiB | Viewed 3318 times ]

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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 30 Mar 2015, 08:35
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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Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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New post 31 Mar 2015, 04:18
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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Re: If four numbers are randomly selected without replacement from set {1, [#permalink]

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

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New post 03 Aug 2017, 02:26
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.

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Re: If four numbers are randomly selected without replacement from set {1,   [#permalink] 03 Aug 2017, 02:26
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