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II-A question 7.27

 
 
Picture of Derek Jiang
II-A question 7.27
by Derek Jiang - Tuesday, 30 January 2018, 9:15 PM
 

P. 7.27: Suppose 3 numbers are chosen from the set {1, 2, ...7}. In how many ways can this be done such that the chosen subset has at least one pair of neighbors?

Hint: Use complementary counting

What does it mean when the question asks "The chosen subset has at least one pair of neighbors."?
 
Picture of David Reynoso
Re: II-A question 7.27
by David Reynoso - Wednesday, 31 January 2018, 10:11 AM
 
Neighbors are numbers that are consecutive. Examples of subsets that have a pair of neighbors would be $\{1,5,6\}$, and $\{2,3,7\}$. Examples of subsets that do not have a pair of neighbors are $\{1,3,5\}$, and $\{2,4,7\}$.
 
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