Eight chairs are in a row. In how many ways can 3 chairs be chosen so that no two chosen chairs are adjacent?
Enter an integer
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Imagine placing 3 chosen chairs among 5 unchosen ones. Between each pair of consecutive chosen chairs we need at least one gap. Place the 3 chosen chairs first with mandatory gaps: this uses up 3+2=5 positions, leaving 3 extra unchosen chairs to place in the 4 available slots (before, between, between, after). This gives (33+3)=(36)=20.