Combinatorial intuition of identity

combinatorics combinations combinatorial-proofs

Hint: Consider forming a committee from a group of $n$ people where one member of the committee is special, e.g. the chairman of the committee. Try counting this in two different ways.

Related

Are Jordan chains always linearly independent?
If $f(z)$ has positive real part, show that $f$ is a constant function.
infimum, supremum of the sequence $\{\sin n\}$
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
Where can I find a review of discrete math
Linear isoparametrics with dual finite elements
$10$ Equations in $10$ variables
An open covering of $\mathbb{Q} \cap [0,1]$ that does not contain any finite subcovering
Proof that a continuous map to $S^n$ whose image is a proper subset of $S^n$ is null-homotopic
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
Finding all real solutions to the equation $3^x+4^x=5^x$
Extended support for Ubuntu 12