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100 Sets 10 Elements Each Union

1425ApprenticeCombinatorics

AMC 12B · 2022 · Problem 6

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

Answer choices

A
40
B
42
C
43
D
49
E
50
0 students attempted0% solvedRating 1425

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