When three cards are randomly selected at a time from a standard deck
of 52 playing cards, what is the probability that all of these three
cards are in the same suit (heart, diamond, spade, or club)?
I'm mortified to ask for help again about probability math. If you look at my profile you probably can see that I've asked several questions about probability. When I thought I can wrap my head around this kind of math, then I had this question and I knew I did not.
Can you please give me some hints on this question and advice me some useful tips for learning to solve this kind of math?
P/s : I already had the answer for this, but I don't know how to solve it!!!
Best Answer
Three cards are selected from a standard deck of $52$ cards. Disregarding the order in which they are drawn, the possible outcomes are $\binom{52}{3}$. Out of these, how many include all cards of the same suit (say hearts)? There are $\binom{13}{3}$ ways in which you can get all 13 heart cards.
Since there are 4 suits, there are $4\binom{13}{3}$ ways in which all cards drawn are of the same suit. Thus the probability is:
$$\frac{4\binom{13}{3}}{\binom{52}{3}}\approx 5.18\%$$