STAT 230: Introduction to Probability and Random Variables
Summer 2009
Problem set: Introduction to Poker
Solutions
PROCEDURE:
We will first choose from the 13 kinds common to each suit, then we choose the suit
for each group of cards that have the same kind.
The total number of poker hands is
52
5
Pair
:
We choose the kind for the pair. There are
13
1
choices for that. Now we have 12 kinds
from which to choose the remaining 3 which works out to be
12
3
combinations. So, the
total number of kind choices for this case is
13
12
1
3
×
.
In choosing the suits, for the pair we have
4
2
choices and for the rest of the cards we
have
4
1
choices each. So, the number of suit choices in this case is
4
4
4
4
1
1
1
2
×
×
×
The total number of hands with one pair is
4
4
4
4
13
12
1
1
1
2
1
3
×
×
×
×
×
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View Full DocumentTwo Pairs
:
We have to choose 2 kinds, one for each pair. We have
13
2
choices there. Then, we have
11
1
kinds left to choose from for the last card. So, the number of kind choices for this
case is
13
11
2
1
×
.
As for the suit choices, we have
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 Fall '08
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 Playing card, total number, Royal Flush

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