Question

A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 7 stocks? How did my textbook get 2187 as the answer?

Answer 1

The total number of possibilities for owning 7 stocks, where each can go up, down, or stay unchanged, is 2187. This is calculated as 3 to the power of 7, because there are 3 possibilities for each stock and 7 stocks in total.

Step-by-step explanation:

The question is asking about the number of possible outcomes when owning 7 stocks, each of which can go up, go down, or stay unchanged. Every stock has 3 possibilities, and since the stocks are independent of each other, we calculate the total number of outcomes by raising the number of possibilities for one stock to the power of the total number of stocks.

To find out how many possibilities there are if you own 7 stocks, you raise 3 (the number of possibilities for one stock: up, down, unchanged) to the power of 7 (the number of stocks you own). This is calculated as 3^7, which equals 2187. Therefore, there are 2187 possible outcomes for the 7 stocks.

Answer 2

Each stock has 3 possibility (either up or down or unchanged)

& you have 7 shares where each one could have the three possibility:

For 1 share you have 3 possibility

for 2 shares you have a total possibility of 3 x 3 =3²

and so on. The total of possibility for 7 shares = 3⁷ = 2187