Question

Investing in stocks. From a list of 15 preferred stocks recommended by your broker, you will select three to invest in. How many different ways can you select the three stocks from the 15 recommended stocks?

Short answer

455

Step-by-step solution

Step-by-Step SolutionStep 1: Introduction

The complementing events is highly useful in calculating event probabilities: The complement of an event A is the event that does not occur, that is, the event that contains all sample points that are not in event A.

Identify the different ways to choose the three stocks from the 15 recommended stocks

In this case, we utilize a combinations formula to choose r stocks from N stocks in ${}^{\mathbf{N}}\mathbf{C}_{\mathbf{r}}$ different ways.

$\begin{array}{l}\mathbf{r}\mathbf{=}\mathbf{3}\\ \mathbf{N}\mathbf{=}\mathbf{15}\end{array}$

role="math" localid="1653485660439" $$\begin{gathered} \mathbf{Total}\mathbf{}\mathbf{different}\mathbf{}\mathbf{ways}\mathbf{=}{}^{15}\mathbf{C}_3 \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{15\times 14\times 13}{3\times 2\times 1} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\frac{2,730}{6} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{455} \end{gathered}$$

Hence, there will be 455 different ways to select the recommended stock.