Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![9. Recall that a deck of cards has fifty-two cards: four suits (Hearts, Diamonds, Spades, and
Clubs) each with thirteen denominations (Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2).
Hearts:
Diamonds:
Spades:
Clubs:
7 6 5 4 3 2
6 5 4 3 2
A K QJ 104 94 86 74 64 54 46 36 26
A♣ K♣ Q4 J4 104 94 84 74 64 54 44 34 24
(a) How many different orderings are there of the entire deck of cards?
AV KV Q♥ J♥ 10 9 8
A K QJ 10 9 8 7
(b) In how many ways are there to have an (unordered) hand of seven cards,
exactly four of which are hearts?
(c) How many five-card hands have at least one King and at least one Spade?
[Hint: Draw a Venn Diagram.]](https://content.bartleby.com/qna-images/question/6d6021e5-396e-45a2-ac2d-b919ebf84add/a792bdb1-2fe9-4821-b1c3-21e8dce2fcba/c2xgwe9_processed.jpeg)
Transcribed Image Text:9. Recall that a deck of cards has fifty-two cards: four suits (Hearts, Diamonds, Spades, and
Clubs) each with thirteen denominations (Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2).
Hearts:
Diamonds:
Spades:
Clubs:
7 6 5 4 3 2
6 5 4 3 2
A K QJ 104 94 86 74 64 54 46 36 26
A♣ K♣ Q4 J4 104 94 84 74 64 54 44 34 24
(a) How many different orderings are there of the entire deck of cards?
AV KV Q♥ J♥ 10 9 8
A K QJ 10 9 8 7
(b) In how many ways are there to have an (unordered) hand of seven cards,
exactly four of which are hearts?
(c) How many five-card hands have at least one King and at least one Spade?
[Hint: Draw a Venn Diagram.]
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