Number Theory
# Factorials

\[ \Large \frac {6! \times 7!}{{10}!} = \ ? \]

\[ \Large \frac{0!+0!+0!+0!}{0!+0!}= \ ? \]

\[\large \left( \frac { 2015!+2016! }{ 2015!\times 2016! } \right) \times 2016! = \ ? \]

\[\Large x! = \frac { (7!)!}{7!}, \ \ \ \ \ \ \ x = \ ? \]

Evaluate

\[\frac{(10!+9!)(8!+7!)(6!+5!)(4!+3!)(2!+1!)}{(10!-9!)(8!-7!)(6!-5!)(4!-3!)(2!-1!)} . \]

**Hint**: You don't need to multiply out all the factorials!

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