This question asks to calculate the number of permutations for 8 objects taken 3 at a time.

Formula for permutations:

The number of permutations is calculated as: $P(n, r) = \frac{n!}{(n - r)!}$ Where:

• $n$ is the total number of objects (8 in this case).
• $r$ is the number of objects taken at a time (3 in this case).

Substituting the values:

$P(8, 3) = \frac{8!}{(8 - 3)!} = \frac{8!}{5!}$

Simplify:

$8! = 8 \times 7 \times 6 \times 5!$ So, the $5!$ cancels out, leaving: $P(8, 3) = 8 \times 7 \times 6 = 336$

Final Answer:

$\text{There are } 336 \text{ permutations.}$

Would you like a breakdown or more examples?

Related Questions:

1. What are permutations and combinations, and how do they differ?
2. How do you calculate factorials, and why are they important in permutations?
3. What happens if $r > n$ in the permutation formula?
4. How is the concept of permutations used in probability problems?
5. Can you calculate $P(10, 4)$ as another example?

Tip:

Always double-check if the problem is asking for permutations or combinations, as the calculations differ significantly.