Showing that the number of ways to select an even number of elements is equal to the number of ways to select an odd number of elements.
21152
Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized
57746
Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
44484
Combinatorial identity $i{n \choose i } =n {n-1 \choose i - 1}$
88628
Proving the total number of subsets of S is equal to $2^n$
123267
Proving that even numbers equal the sum of two odd numbers.
959
Prove that ${{n}\choose{k}} = {{n - 2}\choose{k}} + 2{{n - 2}\choose{k - 1}} + {{n - 2}\choose{k - 2}}$.
6165
Proof by Induction $n^2+n$ is even
47720
Isomorphism from Natural numbers to the Odd Natural numbers
103538
Partitions of $n$ into distinct odd and even parts proof
68882
Path to Combinatorics Problem [$1.11$]
134676
Number of elements of order $p$ is a multiple of $p-1$ (finite group).
13136
Element chasing proof that $(A\setminus C)\setminus(B\setminus C) = (A\setminus B)\setminus C$
107964
Simple combinatorics problem.
135351
$C(n,p)$: even or odd?
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
5089
An element of a group has the same order as its inverse
155372
Find the number of permutations in $S_n$ containing fixed elements in one cycle