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20 Jul 2017, 21:59
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
56% (02:40) correct
44%
(03:12)
wrong
based on 323
sessions
History
Date
Time
Result
Not Attempted Yet
Melilla, Tasha, and Chester plan to fly on a jetliner that has seven seats per row. The middle row consists of three seats, which are separated on each side by an aisle and two seats. The website allows users to choose specific seats, but a computer glitch only assigns rows, not the specific seat within that row. Assuming Melilla plans to book three tickets in the same row, what is the probability that Chester will sit next to Melilla, without any aisle between them?
A. 3/35
B. 1/5
C. 4/21
D. 6/35
E. 1/7
A. 3/35
B. 1/5
C. 4/21
D. 6/35
E. 1/7
20 Jul 2017, 22:31
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_ _ Aisle1_ _ _Aisle 2_ _ is the seating arrangement.
The total ways in which we could pick 2 seats out of 7, is 7c2 = \(\frac{7*6}{2} = 21\)
because there are 7 seats in the same row, and the computer could assign any of the seats.
If they have to sit without any aisle between then,
there are four combinations in which they could be seated without any aisle between them.
They are as follows :
C M Aisle1 _ _ _ Aisle 2 _ _
_ _ Aisle 1 C M _ Aisle 2 _ _
_ _ Aisle 1 _ C M Aisle 2 _ _
_ _ Aisle1 _ _ _ Aisle 2 C M
The probability is \(\frac{4}{21}\)(Option C)
The total ways in which we could pick 2 seats out of 7, is 7c2 = \(\frac{7*6}{2} = 21\)
because there are 7 seats in the same row, and the computer could assign any of the seats.
If they have to sit without any aisle between then,
there are four combinations in which they could be seated without any aisle between them.
They are as follows :
C M Aisle1 _ _ _ Aisle 2 _ _
_ _ Aisle 1 C M _ Aisle 2 _ _
_ _ Aisle 1 _ C M Aisle 2 _ _
_ _ Aisle1 _ _ _ Aisle 2 C M
The probability is \(\frac{4}{21}\)(Option C)
General Discussion
29 Oct 2019, 19:51
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Bunuel
Let’s say the seat numbers are:
AB CDE FG
We see that there are 7C2 = (7 x 6)/2 = 21 ways Chester and Melilla can choose 2 of the 7 seats to sit. However, in order for them to sit next to each other without an aisle between them, they must choose seats AB, CD, DE, or FG. Therefore, the probability they sit next to each other is 4/21. (Note: Tasha is a non-factor here since she can sit at any seat that is not chosen by Chester or Melilla.)
Answer: C
