On this pagePascal TriangleIn Probability, (nk)=(n−1k−1)+(n−1k){n \choose k} = {n-1 \choose k-1} + {n-1 \choose k}(kn)=(k−1n−1)+(kn−1) Proof (n−1k−1)+(n−1k){n-1 \choose k-1} + {n-1 \choose k}(k−1n−1)+(kn−1) =(n−1)!(k−1)! (n−k)!+(n−1)!(n−1−k)! k!= {(n-1)! \over {(k-1)!~(n-k)!}} + {(n-1)! \over {(n-1-k)!~k!}}=(k−1)! (n−k)!(n−1)!