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UGC NET CSE | June 2019 | Part 2 | Question: 7

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How many cards must be selected from a standard deck of $52$ cards to guarantee that at least three hearts are present among them?

  1. $9$
  2. $13$
  3. $17$
  4. $42$
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In this the worst case will happen as follows :-

$1^{st}$ $13*3 = 39$ cards that we pick up turns out to be any one of daimond or spades or clubs but not hearts i.e.

 

Now when we pick the next $3$ cards they are guaranteed to be hearts.($\because$ we have already picked cards from all other suits)

 

$\therefore$ We need to pick $13+13+13+3= 42$ cards in order to guarantee that there are atleast $3$ cards of hearts in the selected cards.

So option $4$ is the correct option.

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