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II-A question 7.27

 
 
JiangDerek的头像
II-A question 7.27
JiangDerek - 2018年01月30日 Tuesday 21:15
 

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."?
 
ReynosoDavid的头像
Re: II-A question 7.27
ReynosoDavid - 2018年01月31日 Wednesday 10:11
 
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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