Answer will be $42$, with pegion hole principle

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+2 votes

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

- $9$
- $13$
- $17$
- $42$

+1 vote

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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