(a) Compute the sums of the squares of Rows 1-4 of Pascal's Triangle. That is, compute:
$\binom10^2 + \binom11^2$
$\binom20^2 + \binom21^2 + \binom22^2$
$\binom30^2 + \binom31^2 + \binom32^2 + \binom33^2$
$\binom40^2 + \binom41^2 + \binom42^2 + \binom43^2 + \binom44^2$
Do these sums appear anywhere else in Pascal's Triangle?

(b) Guess at an identity based on your observations from part (a). Your identity should be of the form
$\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \text{ something}.$
(You have to figure out what "something" is.) Test your identity for $n=1,2,3,4$ using your results from part (a).

(c) Prove your identity using a committee-forming argument.

(d) Prove your identity using a block-walking argument.