The total number of different permutations of a set can be calculated using the factorial of the number of elements in that set. For the set {a, b, c, d, e, f, g}, there are 7 distinct elements.
The formula for calculating permutations is represented as n!, where n is the number of elements in the set. In this case, n is 7.
Thus, we calculate:
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
So, the total number of different permutations of the set {a, b, c, d, e, f, g} is 5040.