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Set A consists of K distinct numbers. If N numbers are selec

by richachampion » Sun Sep 11, 2016 12:14 am
Set A consists of K distinct numbers. If N numbers are selected from the set one-by-one, where N≤K, what is the probability that numbers will be selected in ascending order?


(1) Set A consists of 12 even consecutive integers."‹"‹
(2) N=5

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by GMATGuruNY » Sun Sep 11, 2016 2:49 am
richachampion wrote:Set A consists of K distinct numbers. If N numbers are selected from the set one-by-one, where N≤K, what is the probability that numbers will be selected in ascending order?

(1) Set A consists of 12 even consecutive integers."‹"‹
(2) N=5
Statement 1:
Case 1: n=2
Here, 2 distinct numbers are selected.
The number of orderings in which 2 distinct numbers can be selected = 2!.
Since only one of these 2! ways will be in ascending order, P(ascending order) = 1/2!.

Case 2: n=5
Here, 5 distinct numbers are selected.
The number of orderings in which 5 distinct numbers can be selected = 5!.
Since only one of these 5! ways will be in ascending order, P(ascending order) = 1/5!.

Since the probability can be different values, INSUFFICIENT.

Statement 2:
As illustrated by Case 2, if n=5, then P(ascending order) = 1/5!.
SUFFICIENT.

The correct answer is B.
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by Matt@VeritasPrep » Thu Sep 15, 2016 7:13 pm
Let's try a few sets before going to the answer choices, so we can get a feel for what's happening.

Suppose the set is {1, 2, 3, 4}, and I'm picking two numbers.

I need the first number to be the smaller one, so the probability is 1/2.

OK, now suppose I'm picking three numbers. I need the first to be the smallest (1/3), then the next to be the smaller of the two remaining (1/2), so the probability is 1/6.

Hmmm ... sure looks like my probability is 1/x!, where x is the number that I'm picking. Let's try one more: suppose I'm picking all four numbers. I need the smallest first (1/4), then the smallest of the three remaining (1/3), then the smallest of the two remaining (1/2) ... aha! So it is 1/(4*3*2), or 1/4!, or 1/24.

With that in mind, all I need to know is how many numbers I'm picking, i.e. N, and the answer is 1/N!. That means all statement that gives me N is fine, so S2 alone sufficient.
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