MathDB
SMT 2023 Discrete #5

Source:

May 3, 2023

Problem Statement

Ryan chooses five subsets S1,S2,S3,S4,S5S_1,S_2,S_3,S_4,S_5 of {1,2,3,4,5,6,7}\{1, 2, 3, 4, 5, 6, 7\} such that S1=1|S_1| = 1, S2=2|S_2| = 2, S3=3|S_3| = 3, S4=4|S_4| = 4, and S5=5|S_5| = 5. Moreover, for all 1i<j51 \le i < j \le 5, either SiSj=SiS_i \cap S_j = S_i or SiSj=S_i \cap S_j = \emptyset (in other words, the intersection of SiS_i and SjS_j is either SiS_i or the empty set). In how many ways can Ryan select the sets?