Arrange black and white balls so that each pair of white balls is separated by at least two black balls I am trying to solve the following question: 
How many linear arrangements of $m$ white balls and $(n-m)$ black balls are possible such that each pair of white balls is separated by at least two black balls? The white balls are indistinguishable among themselves and the black balls are indistinguishable among themselves.
Please provide the solution to this.
Thanks,

Make $m$ boxes as shown below (note the "short" last box )  
$\boxed{\circ\bullet\bullet}\;\boxed{\circ\bullet\bullet}\;\boxed{\circ\bullet\bullet} ......... \boxed{\circ}$
Total objects have reduced to $n -2(m-1) = n-2m+2$
Place the boxes among them in $\binom{n-2m+2}{m}$ ways with the "short" box last
