Six pictures are to be arranged from left to right on a wall of an art gallery for display. How many arrangements are possible ?

Answer

To find the number of arrangements of 6 pictures from left to right on a wall of an art gallery, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of pictures**: We have 6 pictures to arrange.

2. **Understand the arrangement process**: When arranging the pictures, for the first position, we have 6 options (since all pictures are available). After placing one picture, we have 5 options left for the second position, 4 for the third, and so on.

3. **Calculate the number of ways to arrange the pictures**:
- For the first position: 6 choices (any of the 6 pictures)
- For the second position: 5 choices (one picture has already been placed)
- For the third position: 4 choices
- For the fourth position: 3 choices
- For the fifth position: 2 choices
- For the sixth position: 1 choice (only one picture left)

4. **Multiply the choices together**:
\[ \text{Total arrangements} = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \]

5. **Recognize the factorial notation**: The multiplication of all integers from 6 down to 1 is represented as \(6!\) (6 factorial).

6. **Calculate \(6!\)**:
\[ 6! = 720 \]

7. **Conclusion**: The total number of arrangements of the 6 pictures is 720.

### Final Answer:
The total number of arrangements possible for the 6 pictures is **720**.