Combination of Non Adjacent Numbers

Context: Undergrad
Thread starter SamitC
Start date Dec 3, 2017
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Combination Numbers

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SamitC

Thread starter
Dec 3, 2017

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?