Let there be a set containing the following digits:
If I choose 5 digit blocks, where the digits are arrange in consecutive ascending order, then the following blocks are possible:
1) 12345 2) 23456 3) 34567 4) 45678 5) 56789
I can intuitively see the pattern, and come up with the following expression to get the number of blocks in a set of digits (where
n is number of digits in the set, and
k is the number of digits in a block):
How can I prove this general equation to be true for all sets and blocks, regardless of their size? In other words, how do I derive this expression analytically rather than intuitively?