I have to count all the possibilities for getting a straight flush in 7 card poker.

I have done this BUT the problem is I have 2 methods which should work, one does, and one doesn't.

The one that works is 4*C(47,2) +36*C(46,2)=41584

The other method involves breaking it up into cases:

i.e. 5 cards straight, 6 card straight, then 7 card straight and added up all those cases.

Anyone have any ideas how to get the 2nd method to work?

I would appreciate any help on this, thank you.