## anonymous 4 years ago Three cards are given to you from a well-shuffled deck of cards. What is the probability that you get all 3 cards from the same suit?

1. anonymous

thirteen choose three over fifty two choose three

2. anonymous

times four

3. anonymous

is this $\frac 1{52 C3}$

4. KingGeorge

Try the method I was talking about a little earlier.

5. KingGeorge

You first need to find the possible ways you can choose three cards from the same suit, and then divide by all the possible three card hands. So you have Construction: Choices: 1. Choose a suit $$\binom41$$ and then 2. Choose a 3 card set from 13 $$\binom{13}{3}$$ So there are $\binom41\cdot\binom{13}{3}$3card hands where all the cards are from the same suit.

6. anonymous

so the probability would be $\frac 1{4 C 1 \times 13 C 3}$

7. KingGeorge

Now we need to find all 3 card hands total. This is just $$\binom{52}{3}$$ (it's a one step process with how I was doing it before). Thus, your probability would be $\Large P=\frac{\binom{4}{1}\cdot\binom{13}{3}}{\binom{52}{3}}$

8. anonymous

probability is.... the possible events over the total right?

9. KingGeorge

We have to divide by the total number of hands to find probability.

10. KingGeorge

Right.

11. anonymous

oh. i get the logic now

12. anonymous

thanks

13. KingGeorge

You're welcome.