How many cards must be selected from a standard deck of 52 cards to guarantee…
2019
How many cards must be selected from a standard deck of 52 cards to guarantee that at least three hearts are present among them?
- A.
9
- B.
13
- C.
17
- D.
42
Attempted by 173 students.
Show answer & explanation
Correct answer: D
Key idea: use the worst-case (pigeonhole) argument: find the largest number of cards you can draw while having at most two hearts.
There are 13 hearts and 39 non-hearts in a 52-card deck.
In the worst case you could draw all 39 non-heart cards and additionally draw 2 hearts, totaling 41 cards and still having only two hearts.
Therefore, drawing one more card (the 42nd) must produce a third heart. So 42 cards are required to guarantee at least three hearts.
Answer: 42
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