Question

A box contains five sets of balls while there are 3 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. 8
• D. 9

Answer 1

let there $s_1,s_2,s_3,s_{4}and{s}_5$ 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 $c_1,c_2,c_3,c_{4}and{c}_5$ be the set of five colours which are unique.
let $s_1=c_1,c_6,c_7$
$s_2=c_2,c_8,c_6$
$s_3=c_3,c_9,c_7$
$s_4=c_4,c_8,c_{10}$
$s_5=c_5,c_{10},c_9$
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.