The number of possible permutations of 8 objects taken 3 at a time can be calculated using the permutation formula:
P(n, r) = n! / (n – r)!
In this case, n is 8 (the total number of objects), and r is 3 (the number of objects to arrange). Let’s plug in the numbers:
P(8, 3) = 8! / (8 – 3)! = 8! / 5!
Now, we need to calculate 8! and 5!:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
5! = 5 × 4 × 3 × 2 × 1 = 120
Now, substituting these values back into our formula:
P(8, 3) = 40320 / 120 = 336
So, the number of possible permutations of 8 objects taken 3 at a time is 336.