# Formulas and Results of Permutations Combinations and Binomial Theorem

1. The factorial of is defined as , where there is a natural number.

2. (Permutation)

3. (Combination)

4.

5.

6.

7.

8. For large , is called the Striling Approximation Formula.

9.

10. , , ,

11. ,

12. If is positive integer, then

13.

14. General Term

15. If is not a positive integer, then the binomial expansion is is called the binomial series.