In how many ways can 4 people be seated in a row containing 6 seats?

Explanation

To find the number of ways to seat 4 people in a row of 6 seats, we can follow these steps:

### Step 1: Determine the number of choices for the first person.
The first person can choose any of the 6 seats.
- **Choices for the 1st person = 6**

### Step 2: Determine the number of choices for the second person.
Once the first person has taken a seat, there are now 5 seats left for the second person.
- **Choices for the 2nd person = 5**

### Step 3: Determine the number of choices for the third person.
After the second person has taken a seat, there are 4 seats remaining for the third person.
- **Choices for the 3rd person = 4**

### Step 4: Determine the number of choices for the fourth person.
Finally, after the third person has taken a seat, there are 3 seats left for the fourth person.
- **Choices for the 4th person = 3**

### Step 5: Calculate the total number of arrangements.
To find the total number of ways to seat the 4 people, we multiply the number of choices for each person:
\[ \text{Total ways} = 6 \times 5 \times 4 \times 3 \]

### Step 6: Perform the multiplication.
Calculating this gives:
\[ 6 \times 5 = 30 \]
\[ 30 \times 4 = 120 \]
\[ 120 \times 3 = 360 \]

### Final Answer:
The total number of ways to seat 4 people in a row of 6 seats is **360**.

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