The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
+1 vote

How many cards must be chosen from a deck to guarantee that at least

  1. two aces of two kinds are chosen.
  2. two aces are chosen.
  3. two cards of the same kind are chosen.
  4. two cards of two different kinds are chosen.
  1. $50, 50, 14, 5$ 
  2. $51, 51, 15, 7$ 
  3. $52, 52, 14, 5$ 
  4. $51, 51, 14, 5$ 
asked in Combinatory by Boss (29.5k points)
retagged by | 1.3k views

1 Answer

+1 vote

since we have to be sure (  guarantee) consider the worst cases for all 

i)two aces of same kind are chosen    (first 48 cards without ace 49th will surely be one kind of  an ace and  50 th will be of another kind of ace

ii) two aces are chosen   first 48 cards without ace then 49th and 50th will definitely be ace

iii)two cards of same kind (here ambiguity is there in question if it is same number then it is 14 if it is same kind then  5 ) all first 13 will be different i.e  of one color either spade or heart  or club or diamond now 14th will surely be of same number of any one of these 13 cards 

iv)2 cards of 2 different kinds   let first 4 are of same number  say all ace or all 2 etc now 5th one will be definitely different number  (if it is same kind then 14)

do ans is A  50 50 14 5

correct option would have been 50 50 5 14

answered by Boss (48.2k points)
edited by

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
49,811 questions
54,527 answers
75,477 users