Find probability of certain number of cards being dealt from remaining cards I did find similar questions to this but I didn't understand the complex answers, so here goes:
I need to find the probability of being dealt a specified amount of cards from the remaining cards in the deck, for example:
I have being dealt 2 cards, Ace and King of clubs, there are now 50 cards remaining in the deck, 11 of which are clubs. I know I can find the probability of the next card dealt being a club by doing:
11 / 50 = 0.22 (22%)

But I need 3 more clubs to make my flush (5 cards of the same suit) and there are 5 cards to be dealt, how do I find the probabilty of being dealt 3 more clubs after 5 more cards have been dealt, would it be something like:
(11 / 50) + (11 / 49) + (11 / 48) + (11 / 47) + (11 / 46)


You can consider clubs as one color and all other cards as another color. Hence you have a two color problem where you draw without replacement. Since you need at least 3 more clubs you also have to consider the cases where you draw 4 or 5 clubs.
So your probability is the sum of drawing exactly, 3,4 or 5 clubs equals
$$\dfrac{\binom{11}{3}\binom{39}{2}}{\binom{50}{5}}+\dfrac{\binom{11}{4}\binom{39}{1}}{\binom{50}{5}}+\dfrac{\binom{11}{5}\binom{39}{0}}{\binom{50}{5}}$$
