The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+14 votes
2.3k views

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. $12$
asked in Combinatory by Veteran (59.6k points)
edited by | 2.3k views
+12
use pigeonhole principle Answer is 2*4+1=9
0
Please re tag this to pigeon hole. I was looking in the GO book under pigeon hole.Its not probability
+1
N=(R-1)*k+1

k = no of pigeon holes

R=expected output here 3

N = minimum number

here we assign an R-1 number of items to k holes and to then add Rth item to any of the holes to get the minimum number
+1
0
Wrong categorization

3 Answers

+25 votes
Best answer
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.
answered by Boss (18.3k points)
edited by
0
may be in first 3 attempt we get same(suits) card and question is asking about minimum.

then A (3) is best choice
+3
minimum in worst case.
+1
But it will not guarantee  that three cards are from same suit. Only Picking 9 or more ( 9 or10 or ......or 52) will guarantee that three cards are from same suit.

Minimum of( 9 ,10, 11...52)= 9, So, 9 is the answer(minimum number of cards to be dealt to guarantee that three cards are from same suit)
+9 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
answered by Loyal (8.1k points)
+4 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?

answered by Active (4.2k points)
0
@shikhar May you please explain your approach more? I find it's correct use of "Expectation".
Answer:

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

42,658 questions
48,639 answers
156,219 comments
63,953 users