A Number That Likes To Grumble

Discrete Mathematics Level 4

How many four digit numbers are there such that each digit is not larger than the previous digit?

Notes: The number "that likes to grumble" is consisted of only natural numbers (0 is not included)

Examples of numbers that likes to grumble:

4321 - each digit is smaller than the neighbouring left digit

4444 - each digit is smaller or is the same as the digit to the left

Number 9788 is not satisfying only because 788 (7 is smaller than eights to the right)

Number 3210 is not satisfying as well, because of 0 (non-natural number)

Bonus: Generalize for \(n\)-digit numbers. Special thanks to Jon Haussmann.


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