Question

question 4
3 pts
in a conference of 47 schools, how many intra - conference baseball games are played during the season if the teams play each other exactly once? hint: in any given game, only two schools can be involved.

Explanation:

Step1: Use combination formula

The number of ways to choose 2 schools out of 47 is given by the combination formula \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 47\) and \(k=2\).

$$C(47,2)=\frac{47!}{2!(47 - 2)!}$$

Step2: Simplify the formula

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Step3: Calculate the result

\(47\times23=(40 + 7)\times23=40\times23+7\times23=920+161 = 1081\)

Answer:

\(1081\)