Combinatorics · Counting with constraints · Multinomial coefficients · Distributions
Two teams, each consisting of \(6\) footballers, have at their disposal \(4\) pairs of shorts and \(4\) jerseys in each of the colours red, blue and white. In how many ways can the footballers dress for the match, every footballer putting on one pair of shorts and one jersey, if each of the two teams must have its own characteristic colour?
Here a colour is called characteristic for a team when every player of that team wears at least one garment of that colour, while no player of the opposing team wears any garment of that colour.
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Serbian Regional Competition 2009, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source