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AMC 10 Mock Exam Discussion For 9/8: Question 9

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AMC 10 Mock Exam Discussion For 9/8: Question 9
by John Lensmire - Friday, September 8, 2023, 1:52 PM

AMC 10 Mock Exam Question 9

The faces of each of $7$ standard dice are labeled with the integers from $1$ to $6$. Let $p$ be the probabilities that when all $7$ dice are rolled, the sum of the numbers on the top faces is $10$. What other sum occurs with the same probability as $p$?

$\textbf{(A) } 13 \qquad \textbf{(B) } 26 \qquad \textbf{(C) } 32 \qquad \textbf{(D) } 39 \qquad \textbf{(E) } 42$

Submit your answer and solution and explanation below! Solutions will be accepted for 48 hours until 9/10 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.