To find the number of possible permutations of 8 objects taken 3 at a time, we use the formula for permutations, which is given by:
P(n, r) = n! / (n – r)!
In this formula, n is the total number of objects, and r is the number of objects taken at a time.
For our question:
- n = 8 (the total number of objects)
- r = 3 (the number of objects taken at a time)
Now, we can calculate the permutations:
P(8, 3) = 8! / (8 – 3)! = 8! / 5!
Calculating 8! gives us:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
And 5! gives us:
5! = 5 × 4 × 3 × 2 × 1 = 120
Now, substituting back into our formula:
P(8, 3) = 40320 / 120 = 336
Thus, the number of possible permutations of 8 objects taken 3 at a time is 336.