Q) 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?
How to solve this question ?
Challenges - Mathematics, Q3 - Pigeon hole
let’s consider we have 6 numbers and out of which take two numbers say a and b ,consider we need to have (a-b) as a multiple of 5 i.e (a-b)%5 =0 this implies (a%5-b%5)=0
i.e. a%5 =b%5 ; this means that out of 6 numbers we have to find the probablity that any two number has same value%5 ,possible values of anyvalue%5 is 0,1,2,3,4 and we have 6 numbers so according to pigeon hole principal we are bound to have two numbers with same value%5,
thus the answer should be 1.
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