2018 AMC 10B Problem 9

The faces of each of 7 standard dice are labeled with the integers from 1 to 6. Let p be the probability 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 p?

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.