I'd like to add my two cents to this as well. At the above, Saka000, unfortunately it's not quite that simple, although you're on the right track. I'll do some rough rounding up/down here so these numbers won't be exact, but they'll be incredibly close.

Like Vorpal mentioned, there's 40 c 4 = 91390 total combinations of 4 cards. This is a very basic calculation:

40! / (4! * (40 - 4)!) = 91390

However, you really don't need to know this figure, or any other exact numbers. All you need to know are probabilities.

**1) At least 1 spade**
To calculate the number of hands which have at least one spade, we simply have to calculate the number of hands that do not have a spade. For this, Saka's calculation is actually almost correct, except you have to subtract that number from 91390. So the chance of not getting a spade is:

29/40 * 28/39 * 27/38 * 26/37 = ~26%.

For every non-spade we draw, there's one less non-spade in there and one less card in the deck. That's how you get to the above calculation, and this applies to all calculations below as well.

Therefore the chance to get at least 1 spade is roughly 1 - .26 = 74%.

**2) At least 2 hearts**
This one is already a bit more complicated. However, this can also be done in a simpler way. You're looking for 2, 3 or 4 hearts. The chance to get 0 hearts can be calculated the same as above:

33/40 * 32/39 * 31/38 * 30/37 = ~44.8%

The chance that you will get exactly one heart is

4 c 1 * 7/40 * 33/39 * 32/38 * 31/37 = ~41.8%

4 c 1 = 4, the reason we add this multiplier in there is because the heart can be drawn in 4 different cases.

Therefore the chance that you'll get 2 hearts or more is roughly 1 - .448 - .418 = 13.4%

**3) At least 3 diamonds**
The calculation for 3 or 4 diamonds is basically the same as the above, except we can now just use the calculations for the chances of getting 3 diamonds and 4 diamonds.

3 diamonds: 4 c 1 * 13/40 * 12/39 * 11/38 * 27/37 = ~8.4%

4 diamonds: 13/40 * 12/39 * 11/38 * 10/37 = ~0.8%

Therefore, the chance of getting at least 3 diamonds is roughly 0.084 + 0.008 = ~9.2%

**4) **I'm not exactly sure which of the two you mean here (same as Vorpal). However, I'm running short on time and the same principles as above apply.

Hopefully that helps!