A box contains five set of balls while there are three balls in each set.each set of balls has one colour which is different from every other set.what is the least number of balls that must be removed from the box in order to claim with certainty that a pair of balls of the same colour has been removed.
a)6
b)7
c)9
d)11

• let there s1 ,s2, s3, s4 and s5 are five set comprising 3 balls each having one colour unique and other two colour must be shared at least once by any one of the other set.
  Let c1,c2,c3,c4 and c5 be the set of five colours which are unique.
  let s1= c1, c6, c7
  s2=c2, c8, c6
  s3=c3, c9, c7
  s4= c4, c8, ,c10
  s5=c5, c10, c9
  thus there are total 10 different colour of balls in five set of balls. so to claim that a pair of same colour of balls has been removed we have to first remove 10 balls and then 1 ball which must be of one of the colour that has been removed earlier.
  so total of 11 balls has to be removed.
• 9 years agoHelpfull: Yes(5) No(3)
• 6 , 1st remove each ball from each set
  nd now again same while taking the 1st ball , some where in that 5 there vll b matching as they asked only pair so it vll b 6
  
  6 is the answer
  
• 9 years agoHelpfull: Yes(5) No(3)
• As we are given that :
  In each set number of balls = 3;
  Total number of sets =5;
  let sets be denoted by set numbers 1,2,3,4 and 5.
  let colours be denoted by A,B,C,D, E, F, G....... so on.
  Therefore,
  1= {A, B, C}
  2= {D, E, B}
  3= {F, G, C}
  4= {H, I, E}
  5= {J, G, I}
  For two balls to be of same colour a colour has to be repeated at least once. So in above sets I have repeated every colour twice in different sets except 5 colours A, D, F, H and J as given to us in the question that each set of balls has one colour which is different from every other set . So we could select colours from A, B................to J i.e 10 colours. (arrange the colours in sets using ur brain and repeat each colour twice so that we can get a pair of same coloured balls except 5 colours A,D,F,H and J and u will find my sets are correct.)
  Now think of the worst case scenario. ........
  If I take out 10 balls from these five sets and all of them turn out to be of different colours i.e A,B, C, D, E, F, G, H, I, J. Then I take out 11th ball, what do you think of its colour?
  I am 110% sure that its colour will be one out of B, C, E, G, I. Because we have colours upto J only and after that colours are repeated. So 11 is the answer.
• 9 years agoHelpfull: Yes(2) No(2)