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在排列组合中，由组合数性质Ｃｍｎ＋１＝Ｃｍｎ＋Ｃｍ－１ｎ，容易推出：Ｃｎｎ＋Ｃｎｎ＋１＋Ｃｎｎ＋１＋Ｃｎｎ＋２＋…＋＋Ｃｎｎ＋ｍ ＝Ｃｎ＋１ｎ＋ｍ＋１．于是 ＣｎｎＰｎｎ＋Ｃｎｎ＋１Ｐｎｎ＋Ｃｎｎ＋２Ｐｎｎ＋…＋Ｃｎｎ＋ｍＰｎｎ＝Ｃｍ＋１ｎ＋ｍ＋１Ｐｎｎ?
In the permutation combination, the combination number property Cmn+1=Cmn+Cm-1n is easily deduced: Cnn+Cnn+1+Cnn+1+Cnn+2+...++ Cnn+m=Cn+1n+m+1. So CnnPnn+Cnn+1Pnn+Cnn+2Pnn+...+Cnn+mPnn=Cm+1n+m+1Pnn?