Letn,s1,s2,...,sn be non-negative integers andM(s1,s2,...,sn)=a1,a2,...,an)|aiis an integer and 0≤ai≤si for eachi∼. In this paper, the cardinality of maximum trees of finite sequences inM(s1,s2,...,sn) is obtained, which generalizes some of Frankl’s results on families of finite sets with prescribed cardinalities for pairwise intersections.