Question

A volleyball league team has fifteen teams. How many different end-of-the-season ranking first, second, and third place are possible. (no ties)

Answer 1

ANSWER

The different ways of ranking the teams is 455 ways

EXPLANATION

Given that;

Note, that any team can be rank first, second, and third

Therefore, we can apply combination to find the number of ways

$\begin{gathered} \text{ }^{15}\text{C}_3\text{ = }\frac{\text{ 15!}}{(15-3)!\text{ 3!}} \\ \\ \text{ }^{15}\text{C}_3\text{ = }\frac{\text{ 15!}}{12!3!} \\ \\ \text{ }^{15}\text{C}_3\text{ = }\frac{\text{ 15 }\times\text{ 14 }\times\text{ 13}}{6} \\ \\ \text{ }^{15}\text{C}_3\text{ = }\frac{\text{ 2730 }}{\text{ 6}} \\ \text{ }^{15}\text{C}_3\text{ = 445 ways} \end{gathered}$

Therefore, the different ways of ranking the teams is 455 ways