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Chapter 11: Problem 21

A stock can go up, go down, or stay unchanged. How many possibilities are there if you own seven stocks?

Short Answer

Expert verified
There are 2187 different possibilities for the outcomes of the seven stocks.

Step by step solution

01

Recognize the possible outcomes

It's essential to understand that each stock has 3 possible outcomes: the stock can either go up, go down, or stay the same. This fact is independent for each of the seven stocks.
02

Apply the Rule of Product

Here we use the rule of product, which states that if there are n ways for one thing to happen and m ways for another to happen, then there are n*m ways for both to happen. So, since each stock has 3 possibilities and there are 7 stocks, there would be \(3^7\) total possibilities.
03

Calculation

Now, we proceed with the calculation. Raise the number of outcomes (3) to the power of the number of stocks (7). So, in mathematical forms: \(3^7 = 2187\).

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