I'wenty-one girls and twenty-one boys took part in a mathematical comp tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem tha both of them solved. Prove that there is a problem that was solved by at least three girls and a
I'wenty-one girls and twenty-one boys took part in a mathematical comp tition. It turned out that (a) Each contestant solved at most six problems, and (b) For each pair of a girl and a boy, there was at least one problem tha both of them solved. Prove that there is a problem that was solved by at least three girls and a
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Twenty-one girls and twenty-one boys took part in a mathematical compe-
tition. It turned out that
(a) Each contestant solved at most six problems, and
(b) For each pair of a girl and a boy, there was at least one problem that
both of them solved.
Prove that there is a problem that was solved by at least three girls and at
least three boys.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2Ffbffb118-9710-4215-bf62-84343774bc46%2F7eqchy_processed.png&w=3840&q=75)
Transcribed Image Text:Twenty-one girls and twenty-one boys took part in a mathematical compe-
tition. It turned out that
(a) Each contestant solved at most six problems, and
(b) For each pair of a girl and a boy, there was at least one problem that
both of them solved.
Prove that there is a problem that was solved by at least three girls and at
least three boys.
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