Total number of non-decreasing numbers with n digits
How many non-decreasing numbers can be generated of n digit length?
Non-decreasing number means the digits from left to right will be in ascending order
123 is non-decreasing 213 is not Say n=1 So non-decreasing numbers will be all the single digit numbers 0 1 2 3 4 5 6 7 8 9 Total number of non-decreasing numbers of 1 digit=10 Now, if n=2 Non-decreasing numbers will be 00 01 02 03 04 05 06 07 08 09 11 12 13 .. So on, Note: numbers with leading 0 is also counted 10 is not included in the list For n=2 Total number of non-decreasing numbers is 55 (List all yourself if you have doubt!)
We will solve this problem with the help of combinatorics
Let's first see, how we can build up the generating function.
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