If ∑25r=0 50Cr ⋅ 50-r C25-r = K(50C25), then K is equal to:

25∑r=0 50Cr ⋅ 50-r C25-r = 25∑r=0 50!/r!(50-r)! × (50-r)!(25)!(25-r)!=25∑r=0 50!/25!25! × 25!(25-r)!(r!) = 50C25 25∑r=0 25Cr =(225)50C25 ∴ K=225