It's the new year at least in my timezone, and to welcome it in, I ask for small representations of the number $2016$.
Rules: Choose a single decimal digit ($1,2,\dots,9$), and use this chosen digit, combined with operations, to create an expression equal to $2016$. Each symbol counts as a point, and the goal is to minimize the total number of points.
Example (my best so far):
$$2016=\frac{(4+4)!}{4!-4}$$
This expression scores 11 points. That is 2 points for the parentheses, 4 points for the $4$s, 1 point for $+$, 2 points for the $!$s, 1 point for the fraction, and 1 point for the $-$.
Allowable actions: basic arithmetic operations (addition, subtraction, multiplication, division), exponentiation, factorials, repeated digits (i.e. if you are working with the digit $7$, you can use $77$ for 2 points), and use of parentheses.
What is the minimum number of points for an expression of the above form equaling 2016, and what are those minimum expressions?
Note that by "Use a single decimal digit" I mean you may only use one of the digits $1$ through $9$, so for example, you can't save in the above expression just by using $8!$ instead of $(4+4)!$ because you would still have the $4!-4$ part.
This question is mostly for fun, but could have some relevance to students who participate in thematic math competitions this year.
Best Answer
With binomial coefficients ($8$ symbols): $$2016={64 \choose 2}={2^{2^2+2} \choose 2}$$ It can be expected that many olympiad problems in $2016$ will use this combinatorial property.
P.S. Special thanks to Alex Fok for minus one symbol in $64$.