4-digit password with unique digits not in ascending or descending order I need to calculate how many possible passwords there are if each password is 4 digits long, using the digits 0-9. All digits in the password must be unique, and cannot all be neither increasing nor decreasing. For example “3569” is not allowed, because the digits are in increasing order, while “1374” is allowed
I know that a four digit password could be anything between 0000 to 9999, hence there are 10,000 combinations. But I am now stuck figuring out how to calculate the number of all possible passwords that are unique, neither increasing nor decreasing. 
I have tried to calculate the possible number of passwords if every digit only may be used once:
$$P(n,r)=\frac{10!}{(10−4)!}=\frac{10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅1}{6⋅5⋅4⋅3⋅2⋅1}=5040$$
But I am now quite sure if this is the answer to the question? If not how should I calculate such a question?

There are $\binom{10}4$ ways to select $4$ distinct digits. 
Under the condition that there is no increasing and no decreasing they can be arranged in $4!-2$ ways. 
So that gives a total of:$$\binom{10}4\left(4!-2\right)$$ possibilities.
