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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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New post 26 Mar 2015, 04:19
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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


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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, 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


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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, 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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New post 26 Mar 2015, 07:22
1
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, 03:40
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
ascendingorder.png [ 18.99 KiB | Viewed 5421 times ]

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

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

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

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New post 30 May 2018, 23:09
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
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Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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New post 01 Jun 2018, 11:25
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.

Answer: D
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Re: If four numbers are randomly selected without replacement from set {1, &nbs [#permalink] 01 Jun 2018, 11:25
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