Consider a standard deck of cards. It has thirteen ranks and four suits. We write these as: R = {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K} and S = {♣, ◇, ♣, ♡} We say that the suit {} are dark, and the suits {♡, ◊} are light. A rank is even or odd according to its numeral. We consider the ranks A, J, Q and K to be neither even nor odd. 1. Write out the following sets. Express your answer as a set using S, R and the set operations: x\U{}. (a) E the even light cards. (b) O the odd dark cards. (c) L the light cards which are not even. 2. Consider five-card hands. By convention, hands of cards are unordered. (a) How many hands contain at most one ♣? For example, {3,5♡, 3◊, K♡, 7♣} is one such hand that meets the above criteria. (b) A full house is a five-card hand with a three-of-a-kind and pair of different ranks. We say that a full house is split if the ranks are not consecutive. Thus {3,5} are split but {7,8} are not. We say that A and K are consecutive. How many split full houses can be formed?
Consider a standard deck of cards. It has thirteen ranks and four suits. We write these as: R = {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K} and S = {♣, ◇, ♣, ♡} We say that the suit {} are dark, and the suits {♡, ◊} are light. A rank is even or odd according to its numeral. We consider the ranks A, J, Q and K to be neither even nor odd. 1. Write out the following sets. Express your answer as a set using S, R and the set operations: x\U{}. (a) E the even light cards. (b) O the odd dark cards. (c) L the light cards which are not even. 2. Consider five-card hands. By convention, hands of cards are unordered. (a) How many hands contain at most one ♣? For example, {3,5♡, 3◊, K♡, 7♣} is one such hand that meets the above criteria. (b) A full house is a five-card hand with a three-of-a-kind and pair of different ranks. We say that a full house is split if the ranks are not consecutive. Thus {3,5} are split but {7,8} are not. We say that A and K are consecutive. How many split full houses can be formed?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Consider a standard deck of cards. It has thirteen ranks and four suits. We write these
as:
R = {A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K} and S = {♣, ◊, ,♡}
We say that the suit
are dark, and the suits {♡, ◊} are light. A rank is even
or odd according to its numeral. We consider the ranks A, J, Q and K to be neither
even nor odd.
1. Write out the following sets. Express your answer as a set using S, R and the set
operations:x\U{}.
(a) E the even light cards.
(b) O the odd dark cards.
(c) L the light cards which are not even.
2. Consider five-card hands. By convention, hands of cards are unordered.
(a) How many hands contain at most one ♣? For example, {34,5♡,3◊, K♡, 7%}
is one such hand that meets the above criteria.
(b) A full house is a five-card hand with a three-of-a-kind and pair of different
ranks. We say that a full house is split if the ranks are not consecutive. Thus
{3,5} are split but {7,8} are not. We say that A and K are consecutive.
How many split full houses can be formed?
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