Respuesta :
Using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.
According to the questions,
Three schools have a chess tournament and four players come from each school. Each player plays against each other from his/her own school.
Formula for Combinations [tex]nC_{r}[/tex] = [tex]\frac{(n-r)!}{r!}[/tex]
[tex]4C_{2}[/tex] = [tex]\frac{4*3}{1*2}[/tex]
= 6
They are 6 ways to select two schools. Given those 2 schools they are
[tex]4^{2}[/tex] = 16 ways to pair up players 1 from each school. They are 3 games played by each of those 3 pairs.
The total number of games played against other school.
6×16×3 = 288.
Similarly using combinations we can find the number of games played against schoolmates. To find this 4 combinations of 2 is 6 ways to select a pair from the 4 people at given school. They are four schools and they play one game each.
6×4×1 = 24
Thus using combinations, the number of games played against schoolmates is 24.
In order to find the number of games of chess are played only if we add the total number of games played against other school and the total number of games played against schoolmates.
288+24 = 312
Hence, using combinations, the number of games of chess played are 312 if each player plays three games against each player plays three games against each player from the other schools, and plays one game against each other.
Learn more about combinations here
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