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A group of students, no two of whom are the same height, are lined up

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Bunuel
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A group of students, no two of whom are the same height, are lined up [#permalink] New post   17 Oct 2020, 13:02
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71% (00:48) correct 29% (00:41) wrong based on 133 sessions
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A group of students, no two of whom are the same height, are lined up next to one another. What is the probability that they are lined up in order from shortest to tallest, from left to right?


(1) There are four students in the group.

(2) Three of the students in the group are females.
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CrackverbalGMAT
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A group of students, no two of whom are the same height, are lined up [#permalink] New post   Updated on: 18 Oct 2020, 09:29
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Bunuel wrote:
A group of students, no two of whom are the same height, are lined up next to one another. What is the probability that they are lined up in order from shortest to tallest, from left to right?


(1) There are four students in the group.

(2) Three of the students in the group are females.




\(Probability = \frac{Favorable \space Outcomes}{Total \space Outcomes}\)

Favorable outcomes = 1 as there is only 1 way in which we can order them from shortest to tallest. To get the probability we need the Total outcomes.


Statement 1:There are four students in the group.

This statement gives us the Total outcomes = 4!

The probability = 1/24


Therefore Statement 1 Alone is Sufficient. Answer options could be A or D



Statement 2: Three of the students in the group are females.

This does not give us the total outcomes as we don't know how many males are there.


Therefore Statement 2 Alone is Insufficient.



Option A

Arun Kumar

Originally posted by CrackverbalGMAT on 17 Oct 2020, 22:32.
Last edited by CrackverbalGMAT on 18 Oct 2020, 09:29, edited 1 time in total.
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IanStewart
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Re: A group of students, no two of whom are the same height, are lined up [#permalink] New post   18 Oct 2020, 06:25
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CrackVerbalGMAT wrote:
Statement 1:There are four students in the group.

This statement gives us the Total outcomes = 4

The probability = 1/4


With 4 students, there are 4! = 24 ways to line up the students, so using Statement 1, the answer is 1/24.
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Re: A group of students, no two of whom are the same height, are lined up [#permalink] New post   18 Oct 2020, 07:37
Given: A group of students, no two of whom are the same height, are lined up next to one another.
Asked: What is the probability that they are lined up in order from shortest to tallest, from left to right?


(1) There are four students in the group.
Favorable ways = 1
Total ways = 4!
Probability that they are lined up in order from shortest to tallest, from left to right = 1/4! = 1/24
SUFFICIENT

(2) Three of the students in the group are females.
The statement does not provide any useful information regarding the probability.
NOT SUFFICIENT

IMO A
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Re: A group of students, no two of whom are the same height, are lined up [#permalink] New post   12 Feb 2021, 21:57
A group of students, no two of whom are the same height, are lined up next to one another. What is the probability that they are lined up in order from shortest to tallest, from left to right?


(1) There are four students in the group.

n = 4

So that means there are 4! ways to order the students. Only 1 of those ways is such that they are ordered from shortest to tallest in ascending order.

P = favourable outcomes / total possible outcomes = 1 / 4! = 1/24

Sufficient

(2) Three of the students in the group are females.

We don't know how many males there are.

Insufficient.

Answer is A.
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Re: A group of students, no two of whom are the same height, are lined up [#permalink]
12 Feb 2021, 21:57
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Bunuel
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