Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.
To determine the total number of matches played, we apply Combination.
ⁿCr = n! / r!( n-r )!
Given that;
We substitute
[tex]^nC_r = \frac{n!}{r!(n-r)!} \\\\^nC_r = \frac{567!}{2!(567-2)!} \\\\^nC_r = \frac{567!}{2!(565)!}\\\\^nC_r = \frac{567 * 566 * 565!}{2!(565)!} \\\\Cancel-common - factor: 565!\\\\^nC_r = \frac{567 * 566 }{2!} \\\\^nC_r = \frac{567 * 566 }{2*1}\\\\^nC_r = \frac{ 320922 }{2} \\\\^nC_r = 160461[/tex]
Given that, 567 teams participate in a football tournament, If each team plays against every other team only once, number of matches played in total is 160461.
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