“ You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one queen and at least one spade. " He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades QA. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four cards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queen spade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades so that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes that the answer is 51C4 + (3 · 12 · 49C3). His answer is incorrect. Explain why, and give the correct answer.
“ You are dealt five cards from a standard deck of 52 cards. How many of these hands have at least one queen and at least one spade. " He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades QA. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four cards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queen spade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades so that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes that the answer is 51C4 + (3 · 12 · 49C3). His answer is incorrect. Explain why, and give the correct answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:“ You are dealt five cards from a standard deck of 52 cards. How many of these hands
have at least one queen and at least one spade. "
He breaks this into two cases. In the first case, he looks at hands which contain the queen of spades
QA. There is 1 way of choosing the Queen of Spades, and 51C4 ways of choosing the other four
cards. In the second case, he will start by choosing a non-spade queen (3 ways) and a non-queen
spade (12 ways). There are 50 cards remaining, so he also throws away the Queen of Spades so
that he doesn't overlap case 1. This gives 49C3 ways of choosing the last three cards. He concludes
that the answer is 51C4 + (3 · 12 · 49C3). His answer is incorrect. Explain why, and give the correct
answer.
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