Question 6
Consider the following $100$ sets of $10$ elements each:
$$
\{1,2,3,\ldots,10\},
$$ $$
\{11,12,13,\ldots,20\},
$$ $$
\{21,22,23,\ldots,30\},
$$ $$
\vdots
$$ $$
\{991,992,993,\ldots,1000\}.
$$
How many of these sets contain exactly two multiples of $7?$
$$
\{1,2,3,\ldots,10\},
$$ $$
\{11,12,13,\ldots,20\},
$$ $$
\{21,22,23,\ldots,30\},
$$ $$
\vdots
$$ $$
\{991,992,993,\ldots,1000\}.
$$
How many of these sets contain exactly two multiples of $7?$