[StevieG]

[ QUOTE ]
So now we try to calculate the possible pairs. There are 13 different ranks that can pair. A pair is 2 suits out of four, so for each rank we have (4 choose 2) 6 pairs avaailable. Hence, 78.

[/ QUOTE ]

D'oh! Lousy brain

You want distinct combinations, not total numbers of pairs.

The number turns out to be 78 but thta's a quirk of teh number. the calcualtion is different.

The number of non-pair combos is
13 (start with any rank)
* 12 (next rank must be different(
/2! (the number of ways to arrange two cards)

which also equals 13*6 or 78.

So total number of starting hands =
13 pairs
+ 78 combos (suited)
+ 78 combos (offsuit)
----
=169