Problem
COM-B2-M03-P005 Complement of a Subset
#5
★★☆☆☆ Level 2 of 5
Prove combinatorially that \(\binom{n}{k}=\binom{n}{n-k}\).
Assign to each set its complement.
To each \(k\)-subset \(A\subseteq[n]\), assign \([n]\setminus A\). It has \(n-k\) elements. The inverse map is again taking the complement, so this is a bijection.
Short, but the inverse map must be stated.