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In this article, we extend Moon's classic formula for counting spanning trees in complete graphs containing a fixed spanning forest to complete bipartite graphs. Let(   X  ,  Y   )$(X,Y)$    be the bipartition of the complete bipartite graphK   m  ,  n${K}_{m,n}$    with∣  X  ∣  =  m$| X| =m$    and∣  Y  ∣  =  n$| Y| =n$   . We prove that for any given spanning forestF$F$    ofK   m  ,  n${K}_{m,n}$    with componentsT  1   ,   T  2   ,  …  ,   T  k${T}_{1},{T}_{2},\ldots ,{T}_{k}$   , the number of spanning trees inK   m  ,  n${K}_{m,n}$    which contain all edges inF$F$    is equal to1   m  n∏   i  =  1   k    (    m  i   n  +   n  i   m   )1  −   ∑   i  =  1   km  i    n  im  i   n  +   n  i   m,$\frac{1}{mn}\left(\prod _{i=1}^{k}({m}_{i}n+{n}_{i}m)\right)\left(1-\sum _{i=1}^{k}\frac{{m}_{i}{n}_{i}}{{m}_{i}n+{n}_{i}m}\right),$wherem  i   =  ∣  V   (   T  i   )   ∩  X  ∣${m}_{i}=| V({T}_{i})\cap X| $    andn  i   =  ∣  V   (   T  i   )   ∩  Y  ∣${n}_{i}=| V({T}_{i})\cap Y| $    fori  =  1  ,  2  ,  …  ,  k$i=1,2,\ldots ,k$   .

Counting spanning trees in a complete bipartite graph which contain a given spanning forest