HMMT 二月 2002 · 冲刺赛 · 第 1 题

英文解析

1. An ( l, a )- design of a set is a collection of subsets of that set such that each subsetcontains exactly l elements and that no two of the subsets share more than a elements. Howmany (2,1)-designs are there of a set containing 8 elements?
   ( )
   Solution: There are = 28 2-element subsets. Any two distinct such subsets have at 8
   most 1 common element; hence, for each subset, we can decide independently whether or 2
   not it belongs to the design, and we thus obtain 2 designs.28