ShinkuDragon Wrote:and i'm lost as to what to do with the 5C2 :X
Well instead of jumping right into the formulas, try understanding how it works first.
You draw 5 cards, they can all be Hearts, Diamonds, Spades, or Clubs.
You draw the first card, it can be any of the 4.
You draw the second card, it can be any of the 4.
...
To have exactly 2 hearts, your hand will look like one of the following combinations, where X means some other suit, and H means Hearts:
- HHXXX, HXHXX, HXXHX, HXXXH
- XHHXX, XHXHX, XHXXH
- XXHHX, XXHXH
- XXXHH
A total of 10, which is the same number as 5C2 (there are 10 ways to choose a combination of 2 items from 5 unique items). The mathematical formula for finding 5C2 is, as shown above, 5!/(2!*(5-2)!), but that's just nuances that don't help with the concept.
Then you find the probability of landing one those combinations. Which means 2 successes and 3 failures, strict.
For cards, it's (0.25)^2 * (0.75)^3 = 0.0263671875 = 2.64%, there are 10 ways this final result can be accepted, so 2.64% * 10 = 26.4%
Note, in your previous post, you said p = 4/52, which is the rate of getting a specific rank, not suit. There are 13 Cards of Hearts to choose from in a deck.
Also note that we're not exactly dealing with recurring cards, so the numbers might be off from a real-life case. If you want the events to be dependent, the probability will be: 5C2 * 13/52 * 12/51 * 39/50 * 38/49 * 37/48, I'm not sure if it should matter when you draw those hearts cards.