Sharp EL-W531X Operation Manual page 26

Permutations, Combinations
<Example 2>
Operation
3
52
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 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,
Hence
13 x
Ways of selecting remaining three cards
Ways of selecting the number: Three types are selected from
(13 - 1) types
(13-1)
Ways of selecting the suit: For each number on the three cards,
Hence
C
12
Ways of selecting five cards
C
52
The probability of drawing one pair is
(13 x C ) x ( C
4 2 12
13 4
2
12
4
5
25
Ways of selecting 5 cards
C
4 2
C
3
there are 4 types of suit 4
3
x 4
3
5
3
x 4 ) C
3 52 5
3
Display
C
4 2