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CBSE Class 10 Answered

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 | 03 Dec, 2017, 01:06: PM
answered-by-expert 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 | 06 Dec, 2017, 01:23: PM
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