Merry Christmas, Magooshers!
Our gift to you? The answer to this week’s Magoosh Brain Twister! (Just what you wanted, am I right?)
Before we give you the answer, take a moment to refresh your memory.
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?
Answer and Explanation
To set up this question, you might want to draw little dashes representing the seats (don’t forget the aisles!), so you can better visualize the problem:
__ __ __ __ __ __ __
The quickest way to think of this problem is as a combinations question. But first, notice that Tasha is not important to the final answer. We essentially are asking how many different ways Melilla and Chester can sit so that they are next to each other (discounting for order, i.e., is Melilla on Chester’s left or right). We will divide this number by the total number of ways Melilla and Chester can sit, discounting, again, for order.
Melilla and Chester could sit in either of two pairs of seats on the edge, or they can sit in the middle row two different ways: one on the left end of the middle row and one in the exact middle, or one on the right end of the middle row and one exactly in the middle. This gives us four different ways:
4/7C2 = 4/21 Answer: (C).
Enjoy your holiday!