$n$ students are standing in a circle. Find the number of ways in which $k$ students can be selected such that no two of them are together.
58749
Choose K items from N in a circle
30625
Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
98082
Another combinatorics problem: $\sum\limits_{k = 0}^n (-1)^k \binom{2n-k}k2^{2n-2k}=2n+1$
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
4505
Number of students in school club : $4$ Circles Venn Diagram Puzzle
39163
Combinatorics : Claude wants to invite 5 people to dinner in a pool of 11 friends, but two of these can't be with each other. How many ways?
94141
$20$ people are sitting around a (circular) table. How many ways can we choose $3$ people, no two of whom are neighbors?
138601
There are $2n+1$ people. For each $n$ people there is somebody who is friend with each of them. Prove there is a "know-them-all" person.
54442
Sum of $k {n \choose k}$ is $n2^{n-1}$
153072
Guessing a subset of $\{1,...,N\}$
118674
Simple upper bound for $\binom{n}{k}$
102235
Choosing $n$ equidistant points on a circle with given radius and center
57221
counting the number of elements in a conjugacy class of $S_n$
139039
Stars and Bars Combinatorics Problem
45448
Minimum number of $k$-partitions of a set of size $n$ to enumerate all $n \choose k$ combinations
51847
Showing that only $(n+1)^{n-1}$ of all the possible $n^n$ choices assure a full car park