14 36 26 Clubs: A4 K4 Q4 J4 104 04 84 74 64 54 14 34 23 (a) How many different orderings are there of the entire deck of cards? (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.]
14 36 26 Clubs: A4 K4 Q4 J4 104 04 84 74 64 54 14 34 23 (a) How many different orderings are there of the entire deck of cards? (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.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d6021e5-396e-45a2-ac2d-b919ebf84add%2Fa792bdb1-2fe9-4821-b1c3-21e8dce2fcba%2Fc2xgwe9_processed.jpeg&w=3840&q=75)
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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