How many different permutations are there of the set {a, b, c, d, e, f, g}?

We will use the concept of permutation and combinations in order to find the number of arrangements.

Answer: The different permutations for the given set {a, b, c, d, e, f, g} is 7! which is 5040.

Let us see how we will use the concept of permutation and combinations in order to find the number of arrangements.

Explanation:

The given set that we have {a, b, c, d, e, f, g} has 7 different elements.

So, let us take 7 different positions that are { 1, 2, 3, 4, 5, 6, 7 }.

At position 1 we can fit 7 elements, at position 2 we can fit 6 elements after we fix one element at position 1.

In a similar way, we can fix 4 elements at position 4 and so on.

Using the permutations formula, the total number of possible permutations/arrangements = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7!

Thus, the different permutations for the given set {a, b, c, d, e, f, g} is 7! which is 5040.