Math 1320
Quiz
Name:__________________________________________ ID number:______________
Instructions: Solve the following problems. Show all your work in order to get full
credit.
For those unfamiliar with playing cards, here is a short description. A standard deck
consists of 52 playing cards. Each card is in one of 13 denominations: Ace, 2, 3, 4, 5, 6,
7, 8, 9, 10, Jack (J), Queen (Q), and King (K), and in one of four suits: hearts (♥),
diamonds (♦), clubs (♣), and spades (♠). Thus, for instance, the Jack of spades, J♠, refers
to the denomination of Jack in the suit of spades. The entire deck of cards is thus
A♥
A♦
A♣
A♠
2♥
2♦
2♣
2♠
3♥ 4♥
3♦ 4♦
3♣ 4♣
3♠ 4♠
5♥
5♦
5♣
5♠
6♥ 7♥ 8♥ 9♥ 10♥
6♦ 7♦ 8♦ 9♦ 10♦
6♣ 7♣ 8♣ 9♣ 10♣
6♠ 7♠ 8♠ 9♠ 10♠
J♥ Q♥
J♦ Q♦
J♣ Q♣
J♠ Q♠
K♥
K♦
K♣
K♠
Problem 1. Find the number of different poker hands of the specified type:
a. Two pairs (two of one denomination, two of another denomination, and one of a
third).
b. Three of a kind (three of one denomination, one of another denomination, and one
of a third).
c. Two of a kind (two of one denomination and three of different denominations).
d. Four of a kind (all four of one denomination and one of another).
e. Straight (five cards of consecutive denominations: A, 2, 3, 4, 5 up through 10, J,
Q, K, A, not all of the same suit.) (Note that the Ace counts either as a 1 or as the
denomination above King.)