I Combination of Non Adjacent Numbers

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The discussion focuses on determining the number of ways to select four non-adjacent numbers from the set {1, 2, 3, 4, 5, 6, 7, 8}. The initial calculation suggests there are five combinations using the formula C(n-r+1,r), resulting in C(5,4)=5. However, upon verification, only four valid combinations are identified: 1,3,5,7; 1,3,5,8; 1,4,6,8; and 2,4,6,8. The participant is unsure about the missing fifth combination and proposes 1,3,6,8 as a potential candidate. The conversation highlights the challenge of accurately counting non-adjacent selections in combinatorial problems.
SamitC
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Suppose there are numbers 1, 2, 3, 4, 5, 6, 7, 8. Question is: How many ways can we pick 4 non adjacent numbers (order does not matter)?
Now, as per formula it is C(n-r+1,r) = C(8-4+1,4) = C(5,4)=5.
Crosschecking, I could find only four: 1,3,5,7 : 1,3,5,8 : 1,4,6,8 : 2,4,6,8
Not sure which 5th one I am missing?
 
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1,3,6,8
 
Thanks.
 

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