This question aims to find how Martha can sit in the** middle seat** when she goes to see a movie with her four friends.

Martha booked** 5 seats** for a movie, **4** for her **friends** and one for herself. They all can sit in **120 possible ways** in those 5 seats considering **one person per seat**. According to the given condition, Martha is sitting in the middle seat which means the** third seat** out of the 5 seats she booked.

She can sit in other seats in many **possible ways**. The **first seat** has **four** possible chances, the **second** **seat** has **three** possible chances, and the **third seat** has only **one**** **possible chance as Martha is sitting in that seat. The **fourth seat** has only **two** possible chances and the last seat which is the **fifth seat** has only **one** chance.

This possible arrangement can be calculated by using factorial calculation. **Factorial** is a way of analyzing the **possible ways** in which an object can be arranged. We can fix an object and find how it can be arranged.

The **product** of all **positive integers** that are less than or equal to the given positive integer is called a factorial. It is **represented** by that positive integer with an **exclamation mark** at the end.

## Expert Answer

We can find the **possible ways** in which Martha can sit in the middle seat by using the factorial approach:

Number of ways = $ 4 \times 3 \times 1 \times 2 \times 1 $

Number of ways can be represented by an integer n:

\[ n = 4 \times 3 \times 1 \times 2 \times 1 \]

\[ n = 24 \]

**Numerical Solution**

There are** 24 possible ways** in which Martha can sit in the middle seat.

## Example

Find the **number of ways** in which the **red toy car** among the other **5** toy cars can be placed in the **third section** of a shelf. There is a space for only **one toy car per section**.

There is a total of **6 sections** on a shelf in which we have to place these cars. They all can be placed in **720 possible ways** in those 6 sections considering one toy car per section. According to the given condition, a **red toy car** is the most **expensive one** that must be placed in the center which means the **third shelf**.

The red toy car must be placed in the third section in many possible ways. The **first section** of the shelf has** five** possible chances, the **second section** has **four** possible chances, and the **third section** has** one** possible chance as a red toy car is placed in that section. The **fourth section** has only **three** possible chances and the **fifth section** has **two** possible chances the last section which is the **sixth section** has only **1** chance.

\[ n = 5 \times 4 \times 1 \times 3 \times 2 \times 1 \]

\[ n = 120 \]

*Image/Mathematical drawings are created in Geogebra. *