Number Theory
Factorials
\[ \Large \frac {6! \times 7!}{{10}!} = \ ? \]
by
Nihar Mahajan
\[ \Large \frac{0!+0!+0!+0!}{0!+0!}= \ ? \]
by
Muhammad Arifur Rahman
\[\large \left( \frac { 2015!+2016! }{ 2015!\times 2016! } \right) \times 2016! = \ ? \]
by
Victor Paes Plinio
\[\Large x! = \frac { (7!)!}{7!}, \ \ \ \ \ \ \ x = \ ? \]
by
Drop TheProblem
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!
by
Curtis Clement