In an experiment comparing the effects of three different fertilizers (A, B, and C) on plant growth, a researcher uses a Balanced Incomplete Block Design (BIBD) where $v=3$ treatments, $b=3$ blocks, $k=2$ treatments per block, and $r=2$ replications per treatment. If $\lambda$ denotes the number of times any pair of treatments appears together in the same block, what is the value of $\lambda$?