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AMC 10 Mock Exam Discussion For 9/24: Question 25

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AMC 10 Mock Exam Discussion For 9/24: Question 25
by John Lensmire - Sunday, September 24, 2023, 12:59 PM

AMC 10 Mock Exam Question 25

A parking lot has 16 spaces in a row. Twelve cars arrive, each of which requires one parking space, and their drivers chose spaces at random from among the available spaces. Auntie Em then arrives in her SUV, which requires 2 adjacent spaces. What is the probability that she is able to park?

$\displaystyle \textbf{(A) } \frac{11}{20} \qquad \textbf{(B) } \frac{4}{7} \qquad \textbf{(C) } \frac{81}{140} \qquad \textbf{(D) } \frac{3}{5} \qquad \textbf{(E) } \frac{17}{28}$

Submit your answer and solution and explanation below! Solutions will be accepted for 48 hours until 9/26 at 2pm Pacific Time. (There's still time for yesterday's problem too: click here.)

Top solutions for all the Mock Exam questions will be collected and shared as part of a full 25 Question Mock AMC 10 Exam.

Note: The question above is a past AMC problem. Solutions submitted must be written by students. Copied solutions will be disqualified.