How many $4$-subsets of $S= \{1,2, \ldots,20\}$ contain no consecutive integers?
34452
In how many ways can you choose $k$ numbers out of $\{1,2,3,\dots,n\}$ so none of them is consecutive?
88628
Proving the total number of subsets of S is equal to $2^n$
147197
Number of connected components of the complement of a compact
156006
Cardinality of set containing all infinite subsets of $\mathbb{Q}$
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
33894
How many chains are there in a finite power set?
91485
Finding an uncountable chain of subsets the integers
113980
Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product
89989
A set of integers whose elements all divide $2015^{200}$ but do not divide each other
119084
How many ordered pairs $(A,B)$ they are if $A$ and $B$ are subsets of $\{ 1,2,3,4,5 \}$ such that $A \cap B = \{1\}$?
45216
Cardinality of $[0,1]$
35692
The set of all finite subsets of the natural numbers is countable
51617
What is the proof that the total number of subsets of a set is $2^n$?
153072
Guessing a subset of $\{1,...,N\}$
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
113668
Uncountable chain of subsets of $\mathbb N$
35648
How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?