Combination of Non Adjacent Numbers

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SUMMARY

The discussion focuses on calculating the number of ways to select 4 non-adjacent numbers from the set {1, 2, 3, 4, 5, 6, 7, 8}. The formula used is C(n-r+1, r), which in this case is C(8-4+1, 4) = C(5, 4) = 5. However, participants identified only four valid combinations: {1, 3, 5, 7}, {1, 3, 5, 8}, {1, 4, 6, 8}, and {2, 4, 6, 8}. The missing fifth combination was suggested to be {1, 3, 6, 8}.

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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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