S.O.S. Mathematics CyberBoard

Say we have a 6/49 lottery.
The ticket has 6 numbers out of 49.
Say the ticket is always sorted from left to right, from smallest number in it to largest.
The differences between those numbers are 5.

What is the total possible count of combinations of these differences?
Order is not important obviously, and also there are no repetitions of numbers in them.

49 48 47 46 45 44 => biggest difference that can be is 44, or, 49 48 47 46 45 - 1 = 44

C(44,5)=1086008 possibilities
preliminary probability of one being extracted (not for any of them actually):
C(5,5)C(39, 0)/C(44,5) = 1/1086008?

I meant to say there are no repetitions in the lottery numbers, the differences between those numbers can have the same cardinality or value

Let be the number of partitions of n into k parts.
Then the number of sequences of differences, treating permutations of a sequence as identical, is

.....

Note that these sequences have greatly varying probabilities.