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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Jaco0318 on February 21, 2021, 09:03:05 pm

Title: Maths Specialist - Pascal's Triangle related questions
Post by: Jaco0318 on February 21, 2021, 09:03:05 pm
Hi I got a problem on solving a Maths question, kindly help.

Prove the identity

2nCn = (nC0)2 + (nC1)2 + .... + (nCn)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?
Title: Re: Maths Specialist - Pascal's Triangle related questions
Post by: fun_jirachi on February 21, 2021, 09:16:51 pm
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 :)