To find the number of permutations of 8 things taken 5 at a time, we can use the formula for permutations, which is:
P(n, r) = n! / (n – r)!
Where n is the total number of items, and r is the number of items to choose.
In this case, we have:
- n = 8
- r = 5
Using the formula, we calculate:
P(8, 5) = 8! / (8 – 5)! = 8! / 3!
Now, we can break down the factorials:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
3! = 3 × 2 × 1 = 6
So now we substitute these values back into the formula:
P(8, 5) = 40320 / 6 = 6720
Therefore, the number of permutations of 8 things taken 5 at a time is 6720.