Problem

2022 AMC 10B Problem 8

Consider the following 100 sets of 10 elements each: \begin{aligned} &\{1,2,3,\ldots,10\}, \\ &\{11,12,13,\ldots,20\},\\ &\{21,22,23,\ldots,30\},\\ &\vdots\\ &\{991,992,993,\ldots,1000\}. \end{aligned} How many of these sets contain exactly two multiples of 7?

\textbf{(A)}\ 40\qquad\textbf{(B)}\ 42\qquad\textbf{(C)}\ 43\qquad\textbf{(D)}\ 49\qquad\textbf{(E)}\ 50


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


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Problem Tags: Counting and probability

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