**1. What is Factorial of a number n, denoted as n!?**

Factorial of any number

Factorial of a number is the product of all the positive integers from 1 up to

n, (including n) (n >= 1)

For example:

Use the

Let us now define

Consider

Now, what does 24 signify?

*
Without allowing any letter to repeat, 24 permutations (arrangements) can be
formed taking all 4 different things at a time*

Caught the point? No? Then Read on

How many ways can you seat four men* a, b, c, d *in four chairs?

Treat the four chairs as the blanks below:

----- ----- ----- -----

Any one of 4 persons can sit in the first chair; any 3 in the 2^{nd}; any 2 in the
3^{rd}; and 1 in the last chair

Filling each chair with a man is one task. And, there are four tasks here.

From rule of counting, the four tasks can be completed in **4.3.2.1** ways, i.e.,

24.

Each of the 24 ways is an arrangement or more popularly a *permutation*

To aid your understanding, listed below are the

So, what does 4! signify?

4! stands for 24 arrangements.

*Another way to define 4! is*

Without allowing things to repeat, the number of ways of arranging 4

different things is 4!.

Generalize 4!. How? As follows:

Definition of n!

Without allowing things to repeat, taking all in each permutation, n
different things can be arranged in **n!** ways.

Note: 0! = 1

**Solved Examples:**

**1. Use factorial formula to simplify:**

Solution:
in the given example write

**10!-8!/8!-7!=8!(10.9-1)/7!(8-1)=8.7!(89)/7!.7=8. 7!(89)/7!.7=89/7**