no of ways to create a calendar for 3-part summer camp
Source: VII - Mathematics Regional Olympiad of Mexico Northeast 2007 P1
September 17, 2022
combinatorics
Problem Statement
In a summer camp that is going to last weeks, you want to divide the time into periods so that each period starts on a Monday and ends on a Sunday. The first period will be dedicated to artistic work, the second will be for sports and in the third there will be a technological workshop. During each term, a Monday will be chosen for an expert on the topic of the term to give a talk. Let be the number of ways in which the activity calendar can be made. (For example, if one way the calendar could be done is by putting the first four weeks for art and the artist talk on the first Monday; the next weeks could be for sports, with the athlete visit on the fourth Monday of that period; the remaining week would be for the technology workshop and the talk would be on Monday of that week.) Calculate .