Question 1094482
<br>The language you use is not standard mathematical terminology; so I'm not sure what you are asking.  It appears you ar simply looking for the number of ways of writing 6 numbers from 1 to 49 inclusive so that the 6 numbers are increasing order.<br>
If that is what you are after, then the number is simply "49 choose 6", 49C6, which is
{{{(49*48*47*46*45*44)/(6*5*4*3*2*1) = 13983816}}}<br>
That number is the number of ways you can choose 6 of 49 numbers without regard to order; once you have chosen a particular 6 numbers you can simply put them in ascending order.<br>
You can also arrive at the same number by choosing any 6 numbers in sequence; the number of ways of doing that is
{{{49*48*47*46*45*44 = 10068347520}}}<br>
Then, having chosen some set of 6 numbers, there are 6! = 6*5*4*3*2*1 = 720 different ways to arrange them, of which only one way has them in increasing order; so the number of sequences of 6 numbers in increasing order is
{{{10068347520/720 = 13983816}}}