Question

consideration is being given to forming a super ten basketball conference. the top 10 university basketball teams in the country, based on past records, would be members of the super ten conference. each team would play every other team in the conference during the season and the team winning the most games would be declared the national champion. how many games would the conference commissioner have to schedule each year? (remember, mcmaster versus alberta is the same as alberta versus mcmaster.)

a. 125
b. 14
c. 45
d. 50

Explanation:

Step1: Identify combination scenario

We need the number of unique pairs of teams, since each pair plays once. This is a combination problem, calculated by the formula for combinations: $C(n,k)=\frac{n!}{k!(n-k)!}$, where $n=10$ (total teams) and $k=2$ (teams per game).

Step2: Substitute values into formula

$$C(10,2)=\frac{10!}{2!(10-2)!}$$

Step3: Simplify the factorial expression

$$C(10,2)=\frac{10\times9\times8!}{2\times1\times8!}=\frac{10\times9}{2}$$

Step4: Calculate the final value

$$\frac{90}{2}=45$$

Answer:

c. 45