Question

A college's soccer team will play 20 games next fall. Each game can result in one of 3 outcomes: a win, a loss, or a tie. Find the total possible number of outcomes for
the season record.
Answer
Kevnad

Answer 1

Using the Fundamental Counting Theorem, it is found that there are 3,486,784,401 possible number of outcomes for the season record.

What is the Fundamental Counting Theorem?

It is a theorem that states that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem, there are 20 games, each with 3 outcomes, and games are independent, hence:

$n_1 = n_2 \cdots = n_{20} = 3$

Then:

$N = 3^{20} = 3486784401$

There are 3,486,784,401 possible number of outcomes for the season record.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866