Help with kind of weird odds calculations

Hello. I'm looking to perform a study on a site's shuffling and help with any of these calculations would be extremely appreciated.

It might be painfully obvious but I want to make sure I do this right, and I'm a bit stumped.

How would I calculate the odds of the community (basically any random 5 cards) having at least one pair among it? I can figure it out if it's one specific card, but as far as there being one pair among any of the 5 cards, I'm not quite sure how to go about calculating it.

Similarly, I want to know how I'd calculate the odds of the community (any 5 cards) holding three of the same suit. The suit does not matter.

And with these two odds, could I then figure out the odds of any 5 cards having EITHER a pair or flush draw?

I don't know if these are difficult calculations or if they're just more obvious than I'm seeing, but I thank anyone who will help.

if you give me an hour or so (i'm busy with a tourney right now - very distracted) i can show you how to calculate that with 'combinations'
I'm currently trying to find an old thread about that actually but having trouble with distractions

Alright thanks, I appreciate it.

using combinations is a good way of figuring out the odds of certain situations

Here's Brian Alspach's website; he's a prof at the simon frasier university and also happens to be a poker fanatic aswell
credit goes to Four Dogs who gave me this great link.

http://www.math.sfu.ca/~alspach/computations.html

Search the site and you'll find almost every kind of board and he explains how it is calculated, and what the odds of that kind of board happening are.

Hope this helps.

That's perfect. Thank you kindly.

no problemo