The total possible number of arrangements is $\dfrac{8!}{2^4}$.

The number in the one's are together is equal to $\dfrac{7!}{2^3}$

Inclusion/exclusion $\displaystyle\sum\limits_{k = 0}^4 {{{\left( { - 1} \right)}^k}\dbinom{4}{k}\dfrac{{\left( {8 - k} \right)!}}{{{2^{4 - k}}}}} $