Concentration inequality on 1-norm of random vector

Question

I would like to give an upper bound on $\Pr\{||X-\mathsf{E}[X]||_1 > t\}$ where $X$ is a $d$-dimensional random vector with each entry follows i.i.d. binomial $(n,p)$ (so $\mathsf{E}[X]$ is actually a vector with all entry $np$), I found some results about matrix concentration inequalities (such as matrix Berstein) but they are all on 2-norm. Any references about this kind of result on 1-norm?