Math Homework Help

Imagine you have an infinite amount of five different banknotes (10 euros, 50,100,200,500). You have to put them in a box and find all possible types(modes) of doing that. Rules are:

 After 10 euros you must put a banknote of 50 or 100 

After 50 euros you must put a banknote of 10 or 200

 After 100 euros you must put a banknote of 10 or 100 

After 200 euros you must put a banknote of 50 or 500

 After 500 euros you must put a banknote of 200 or 10

 Every time you get a number of how many banknotes you have to put.

 For example: You have to put 3 banknotes:

 All the possible combinations are: 

(10,50,10) (10,50,200) (10,100,10) (10,100,100) 

(50,10,50) (50,10,100) (50,200,50) (50,200,500) 

(100,10,50) (100,10,200) (100,100,10) (100,100,100)

 (200,50,10) (200,50,200) (200,500,200) (200,500,10) 

(500,200,50) (500,200,500) (500,10,50) (500,10,100) 

The number of possible combinations is 20. What are the total number of combinations if one draws ‘n’ banknotes?