Combinatorics is a branch of math focused on arrangements ofobjects. Jorge is an event organizer who must seat 102 guests.He has circular tables that seat 10 people each and square tablesthat seat 4 people each. He wants to use as many circular tablesas possible but have no empty seats. Explain how he couldarrange the tables he will need.Activity

Answer:He needs 9 circular tables and 3 square tables.Step-by-step explanation:Given:Number of persons in each circular table = 10Number of persons in each square table = 4Now, in order to maximize number of circular tables, we must find the maximum multiple of 10.Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100.Now, if we take 100, then the seats remaining are 2. But the square tables require 4 persons. So, 100 is not correct.Next, if we choose 90 as a multiple of 10, then the circular tables used would be [tex]\frac{90}{10}=9[/tex]. Now, number of guests left are 102 - 90 = 12. Now, 12 is a multiple of 4. So, 3 square tables can accommodate 12 persons as [tex]4\times 3=12[/tex].Therefore, he has to use 9 circular tables and 3 square tables to maximize the number of circular tables.