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

**Solution:**

**Suppose you need to arrange n people in a row. How many distinct arrangements are possible?**

**We have n options to fill the first chair, (n − 1) (n − 1) options to fill the second chair, (n − 2) (n − 2) options to fill the third chair, and so on.**

**Thus, using the FPC (Fundamental Principle of counting), the total number of arrangements of the n people in the row of n chairs is**

**(n) × (n − 1) × (n − 2) ×... × 1 = n! (n) × (n − 1) × (n − 2) × ... × 1 = n!**

**Each particular arrangement is termed as a permutation of the n people**

**Hence, there will be a total of n! different permutations / arrangements.**

**Let us proceed with the given problem:**

The number of ways in which the 7 elements of the given set can be arranged is 7!.

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040 ways

The logic for the above is as follows:

There are seven positions for seven letters belonging to the set.

Any position can be filled in 7 ways.

But once the position is filled then the next position can be filled six ways,

the next position can be filled in 5 ways and so on.

7 |
6 |
5 |
4 |
3 |
2 |
1 |

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

**Summary:**

Permutations basically imply arrangements. The set which comprises 7 elements a, b, c, d, e, f, g are to be arranged and this can be done in 7! or 5040 ways.