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Pigeonhole Principal II?
Each of the 40 participants in an art workshop signed up for one or more of the following courses; Handicraft, Ceramics and Chinese Paintings. How many participants signed up for the same courses?
earlier i asked another question regarding this. I understand the concept, but i don't really understand this question. Can help?
had the 40 participants signed up once only then
their distribution to the courses would be like
13 - 13 - 14
but then ... participants can join in more than one course
thus there would be a minimum of 13 participants and a maximum of 40 participants in one course.
Edit:
i think i misunderstood the question initially.
we are looking for the number (i guess the minimum) of people having the same choices.
there would be 8 elements in the power set of a tripleton.
thus there would be 7 possible choices:
H
C
P
HC
HP
CP
HCP
then if the people are evenly divided ...
40/7 = 5 ... with some remainders ...
thus we are guaranteed that there are at least 5 people going to the same set of courses.
A Year of Swedish Handcraft: Ceramic Tile.mp4