Six distinct positive integers are randomly chosen between 1 and 2006, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of 5?
1.3/5
2.1/2
3.4/5
4.1
//I have not get that how here we can apply pigeonhole principle to solve the question and how we can solve this question
For two numbers to have a difference that is a multiple of 5, the numbers must be congruent 
(their remainders after division by 5 must be the same).
are the possible values of numbers in . Since there are only 5 possible values in and we are picking 
numbers, by the Pigeonhole Principle, two of the numbers must be congruent .
Therefore the probability that some pair of the 6 integers has a difference that is a multiple of 5 is 
.
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