Final answer:
The 10th number in the third diagonal of Pascal's triangle is 55, which corresponds to the entry C(11, 2). The provided options do not match the correct answer, indicating an error in the question or choices.
Step-by-step explanation:
The question asks, 'What is the 10th number in the third diagonal of Pascal's triangle?' To answer this, let's first understand the structure of Pascal's triangle. Each number in Pascal's triangle is the sum of the two numbers directly above it in the previous row. The third diagonal refers to the entries of the form C(n, 2), which essentially counts the ways to choose 2 items out of n, where n is the row index starting from 0.
To find the 10th number in the third diagonal, we must consider the entry C(9 + 2, 2), since the top of Pascal's triangle is row 0. This gives us C(11, 2) which is 55. It seems that there might have been a confusion in the options provided for this question, because none of the choices matches the correct answer, 55. It's possible that the question intended to ask for a different diagonal or a different element in the third diagonal.