Lecture 4
Section 1.8: Combinations II
Example 1.8.5 Playing Cards.
A deck of 52 cards containing 4 aces is shuffled thoroughly and the cards are
distributed among 4 players so that each player receives 13 cards. We shall
determine the probability that each player will receive one ace.
Method 1:
p
1
= the probability that the 1
st
player receives one ace =
1
4
12
48
/
13
52
;
p
2
= the probability that the 2
nd
player receives one ace from the remaining deck
=
1
3
12
36
/
13
39
;
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3
= the probability that the 3
rd
player receives one ace from the remaining deck
=
1
2
12
24
/
13
26
;
p
4
= the probability that the
2nd
player receives one ace from the remaining deck
=
1
1
12
12
/
13
13
.
p =
p
1
p
2
p
3
p
4
= [(13)
4
(4!)(48!)]/52!
Method 2 (book’s method) :
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 Spring '08
 Staff
 Probability, Playing card, Card game

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