# Find the probability of drawing a full house from a set of 52 cards?

MAth problem above. Thanks

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• QC
Lv 7
9 years ago

Total number of hands: (52 C 5) = 2,598,960

Full house: 3 of a kind + 2 of a kind

3 of a kind could be one of 13 different values

For each of these, there are (4 C 3) ways to choose 3 cards

2 of a kind could be one of 12 remaining values

For each of these, there are (4 C 2) ways to choose 2 cards

Number of hands that are full houses

= 13 * (4 C 3) * 12 * (4 C 2) = 13*4 * 12*6 = 3744

Probability of drawing a full house = 3744/2,598,960 = 0.001440576 = 0.144%

• Anonymous
9 years ago

ok thre is 52 cards and there are 4 of each number so you would divide 52 by 4 and get 13 so that means there are 13 cards for each set not you would times 52 and 13 and get 676, so there are 676 different ways to get a full house. is that what your asking for?

• 3 years ago

The are 4 aces in a properly-recognized deck of fifty two taking part in cards. So on a single draw (if the deck is complete) you have a 4 in fifty two possibility of pulling an ace, which reduces to one million in 13. precis: one million in 13 (or 4 in fifty two) this is a 7.6923% possibility.

• 9 years ago

This is a product of combinatorics.

A full house is 3 of a kind and 2 of a kind e.g. 77733

How many ways can you pick the first card: 13C1 = 13

How many ways can you get 3 more of the same card: 4C3 = 4

How many ways can you pick the other kind: 12C1 = 12

How many ways can you get 2 more of the same card: 4C2 = 6

Multiply these out: 3744.

How many different hands can be dealt 52C5 = 2,598,960

The quotient of these two is 0.144 %