# Math Help - Probability -dealing with cards

1. ## Probability -dealing with cards

This question is on a final exam study sheet. Here it is: What is the probability of getting a full house ( 3 of one number and 2 of another) from 5 cards dealt from a shuffled deck of 52 playing cards?

Not sure quite how to attack this ... permutation? combination? etc

2. Originally Posted by RotundRaspberry
This question is on a final exam study sheet. Here it is: What is the probability of getting a full house ( 3 of one number and 2 of another) from 5 cards dealt from a shuffled deck of 52 playing cards?

Not sure quite how to attack this ... permutation? combination? etc
Read this: Poker probability - Wikipedia, the free encyclopedia

3. Hello, RotundRaspberry!

Card games are usually combinations
. . since the order of the cards makes no difference.

What is the probability of getting a Full House (3 of one number and 2 of another)
from 5 cards dealt from a shuffled deck of 52 playing cards?

There are 13 choices for the value of the Triple.
There are: . $_4C_3 \,=\,{\color{blue}4}$ ways to get the Triple.

There are 12 choices for the value of the Pair.
There are: . $_4C_2 \,=\,{\color{blue}6}$ ways to get the Pair.

Hence, there are: . $13\cdot 4\cdot12\cdot 6 \;=\;{\color{blue}3,\!744}$ possible Full Houses.

There are: . $_{52}C_5 \;=\,2,\!598,\!960$ possible 5-card Poker hands.

Therefore: . $P(\text{Full House}) \;=\;\frac{3744}{2,\!598,\!960} \;=\;\frac{6}{4165}$