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\frac{355687428096000}{7!\times 10!}
The factorial of 17 is 355687428096000.
\frac{355687428096000}{5040\times 10!}
The factorial of 7 is 5040.
\frac{355687428096000}{5040\times 3628800}
The factorial of 10 is 3628800.
\frac{355687428096000}{18289152000}
Multiply 5040 and 3628800 to get 18289152000.
19448
Divide 355687428096000 by 18289152000 to get 19448.