To calculate the product of these permutations, you can use the formula for permutations:
- **P(8, 5)**: This means "the number of ways to arrange 5 items out of 8." You can calculate it by dividing 8 factorial (8!) by 3 factorial (3!).
- **P(7, 4)**: This means "the number of ways to arrange 4 items out of 7." You can calculate it by dividing 7 factorial (7!) by 3 factorial (3!).
- **P(6, 5)**: This means "the number of ways to arrange 5 items out of 6." You can calculate it by dividing 6 factorial (6!) by 1 factorial (1!).
Now, let's calculate each factorial:
- **8!** is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 40,320.
- **7!** is 7 x 6 x 5 x 4 x 3 x 2 x 1, which equals 5,040.
- **6!** is 6 x 5 x 4 x 3 x 2 x 1, which equals 720.
Now, divide to find the product of these permutations:
**P(8, 5) · P(7, 4) · P(6, 5)** can be calculated as **(8! / 3!) * (7! / 3!) * (6! / 1!)**.
Now, calculate the product:
(40,320 / 6) * (5,040 / 6) * 720 equals 4,581,888,000.
So, the product of the permutations P(8, 5) · P(7, 4) · P(6, 5) is 4,581,888,000.