Bunuel wrote:

On a certain airline, customers are assigned a row number when they purchase their ticket, but the four seats within the row are first come, first served during boarding. If Karen and Georgia end up with random seats in the same row on a sold-out flight, what is the probability that they sit next to each other?

A. 25%

B. 40%

C. 50%

D. 75%

E. 80%

In a row of 4 seats, there are 4! = 24 sitting arrangements for 4 people. Now let’s find the number of ways that Karen (K) and Georgia (G) will be sitting next to each other. Let’s designate the other two passengers as A and B, and they are sitting in the same row as Karen and Georgia. The arrangement could be as follows:

[KG]-[A]-[B]

Since K and G are sitting next to each other, we can count [KG] as one person, such that there are 3 people sitting in the same row, and thus the number of ways to arrange those 3 people is 3! = 6. However, since we can arrange KG in 2! ways (KG or GK), the number of ways to arrange the “3 people” is actually 2 x 6 = 12. Thus, the probability that Karen and Georgia are sitting next to each other is 12/24 = 1/2 = 50%.

Answer: C

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Founder and CEO

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