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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: 65194
If four numbers are randomly selected without replacement from set {1,  [#permalink]

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26 Mar 2015, 03:19
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15% (low)

Question Stats:

81% (00:53) correct 19% (00:48) wrong based on 171 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.

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Posts: 488
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, 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

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

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Posts: 8757
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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26 Mar 2015, 04:29
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
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Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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26 Mar 2015, 06:22
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
Joined: 02 Sep 2009
Posts: 65194
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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30 Mar 2015, 02:40
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 [ 18.99 KiB | Viewed 10890 times ]

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

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

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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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Posts: 58
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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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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Posts: 1670
Re: If four numbers are randomly selected without replacement from set {1,  [#permalink]

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30 May 2018, 22:09
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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01 Jun 2018, 10:25
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.

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

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28 May 2020, 18:18
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Re: If four numbers are randomly selected without replacement from set {1,   [#permalink] 28 May 2020, 18:18