SOLUTION: How many series of 06 numbers can be made of 1 to 49,where each and every number should be related to each and every series...I.e if we pick 1,14,22,37,39,45 then all the numbers s

Question 1094482: How many series of 06 numbers can be made of 1 to 49,where each and every number should be related to each and every series...I.e if we pick 1,14,22,37,39,45 then all the numbers should fall in the same series in sequence....thanx
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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.

If that is what you are after, then the number is simply "49 choose 6", 49C6, which is

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.

You can also arrive at the same number by choosing any 6 numbers in sequence; the number of ways of doing that is

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

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