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39 votes
39 votes

The minimum number of cards to be dealt from an arbitrarily shuffled deck of $52$ cards to guarantee that three cards are from same suit is

  1. $3$
  2. $8$
  3. $9$
  4. $12$
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6 Answers

Best answer
42 votes
42 votes
There are $4$ sets of cards. So, up till $8$ cards there is a chance that no more than $2$ cards are from a given set. But, once we pick the $9$$^{th}$one, it should make $3$ cards from any one of the sets. So, $(C)$ is the answer.
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23 votes
23 votes
As suggested above also

apply pigeon hole, 4 holes (suits)

n pigeons(no of cards to be drawn)

floor [(n-1)/p] +1=3

floor[(n-1)/4]  =2

(n-1)/4  >= 2

n>=9

minimum 9 cards must be picked
9 votes
9 votes

Any corrections or questions  to my solution are welcome

 

5 votes
5 votes

Can this question be solved by calculating expectation:
Expectation of getting three cards from same deck->

E(x) = 13*(13/52) + 12*(12/51) + 11*(11/50)
       =  8.49 => 9 cards

Hence is the answer.
Is it correct?

Answer:

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