How to Use the Factorial Notation

We have had several discussions about the factorial notation, so I think this introduction is a bit late. However, it is important that you know these basic facts in order to perform calculations and understand better in later discussions.

The factorial of a non-negative integer n is the product of all the positive numbers less than n. For example, the

4! = 4 \times 3 \times 2 \times 1 = 24.

and

5! = 5 \times 4 \times 3 \times 2 \times 1 = 120.

In Introduction to Permutations, we have discussed that there are n! ways to arrange n distinct objects into a sequence. For instance, if we have 3 objects namely A, B, and C, then they can be arranged in 3! = 3 \times 2 \times 1 = 6 ways. The arrangement are as follows:

ABC, ACB, BAC, BCA, CAB, CBA.

 We have also learned some reasons why mathematicians chose the definition 0! = 1. » Read more

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