We have 2 racks with holding holes. Rack 1 holds red balls and rack 2 holds white balls. Each rack has holes along its length where a ball can be present. Along both racks each hole is either empty with probability $1-p$ or holds 1 ball with $p \in (0,1)$ independently. Integers m and n are fixed and are smaller than number of holes in each rack. Balls contained within first m holes in rack 1 and first n holes in rack 2 are placed in an urn. Let X be the number of red balls in urn and Y be number of white balls in urn and Z be total number of balls in urn.
I know X~Bin(m,p) and Y~Bin(n,p) and Z=X+Y~Bin(m+n,p).
How do I find E(XZ)?