The number of different permutations of a set is calculated by taking the factorial of the number of elements in the set. In this case, the set is {a, b, c, d, e, f, g}, which contains 7 distinct elements.
The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n. Therefore, to find the number of permutations of the set, we need to calculate 7! (7 factorial).
Calculating 7!:
- 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1
- 7! = 5040
Thus, there are a total of 5040 different permutations of the set {a, b, c, d, e, f, g}.