Maths Specialist - Pascal's Triangle related questions

[Jaco0318]

Hi I got a problem on solving a Maths question, kindly help.

Prove the identity

²ⁿC_n = (ⁿC₀)² + (ⁿC₁)² + .... + (ⁿC_n)²

HINT: Consider an urn containing n white balls and n red balls, i.e. 2n balls altogether. In how many ways can you select n balls?

[fun_jirachi]

When picking n balls from n red and n white, we can start by picking n red and zero white. There are \(\binom{n}{n} \times \binom{n}{0}\) ways of doing so. We can also pick n-1 red and 1 white for which there are \(\binom{n}{n-1} \times \binom{n}{1}\). Try continuing this pattern, noting also that \(\binom{n}{k} = \binom{n}{n-k}\).

Hope this helps