Vanshee has randomly chosen eight distinct numbers from the first 2016 natural numbers.What is the probability that some pair of numbers of the chosen eight has a difference which is divisible by 7?

Asked by sivakumaranm | 3rd Dec, 2017, 01:06: PM

Expert Answer:

begin mathsize 16px style Here space we space are space considering space just space one space pair space of space number space is space required space out space of space 4 space pairs
now space from space number space form space 1 space to space 2016
there space are space 288 space nos. space of space the space category space 7 straight k space left parenthesis divisible space by space 7 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 1 space left parenthesis leaves space remainder space 1 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 2 space left parenthesis leaves space remainder space 2 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 3 space left parenthesis leaves space remainder space 3 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 4 space left parenthesis leaves space remainder space 4 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 5 space left parenthesis leaves space remainder space 5 right parenthesis
there space are space 288 space nos. space of space the space category space 7 straight k plus 6 space left parenthesis leaves space remainder space 6 right parenthesis
now space inorder space to space get space difference space divisible space by space 7 space the space two space nos. space should space come space from space same space group
selecting space 2 space nos space from space same space group space is space straight C presuperscript 288 subscript 2 space and space we space have space 7 space groups
ans space will space be space fraction numerator straight C presuperscript 288 subscript 2 cross times 7 cross times straight C presuperscript 2014 subscript 6 over denominator straight C presuperscript 2016 subscript 8 end fraction
NOTE colon space this space sum space is space out space of space your space syllabus space end style

Answered by Arun | 6th Dec, 2017, 01:23: PM