13 x
4
C
2
12
C
3
x 4
3
4
3
52
5
<Example 2>
Find the probability of drawing one pair when 5 cards are
drawn from a deck of 52 cards.
No jokers are included in the deck.
Probability of drawing one pair =
Ways of selecting one pair Ways of selecting 5 cards
Ways of selecting one pair =
Ways of selecting two cards to make a pair x Ways of selecting
3 remaining cards
Ways of selecting two cards to make a pair
Ways of selecting the number: 13 possibilities from 1 to 13 (King)
Ways of selecting the suit: Two suits selected from four,
4
C
2
Hence
Ways of selecting five cards
52
C
5
The probability of drawing one pair is
(13 x
4
C
2
) x (
12
C
3
x 4
3
)
52
C
5
Ways of selecting remaining three cards
Ways of selecting the number: Three types are selected from
(13 - 1) types
(13-1)
C
3
Ways of selecting the suit: For each number on the three cards,
there are 4 types of suit 4
3
Hence
Operation Display
413
12
2
25
Permutations, Combinations
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