Re: HSC 2013 4U Marathon
can someone explain the perms/combs 2008 q7a
i) U want 3 balls of the same colour. FIRST THING U GOTTA DO, is pick a colour which u want to "replicate" three times. So 3c1, three colours. You want to have three balls out of n balls, so times that by nC3.
You divide this by the total number of possibilities, which is choosing three balls out of 3n balls, THIS IS BECAUSE you have n balls of each colour, and 3 colours, so 3nC3.
ii) Here you want to choose 1 ball of each colour, (all different colours) so you choose 1 from n, ie nC1, and you do this for each colour, so nC1^3, and again, divide by total possibilities, which is 3nC3.
iii) Here, you want to choose 1 colour, and have 2 balls of that colour, then choose another colour FROM THE TWO THAT REMAIN, to have 1 ball of one of those colours. So 3C1 for one colour, and u choose 2 balls from n balls, so nC2. To choose the remaining ball, you can choose from 2 colours, so pick one as per 2C1, and you choose 1 ball of that colour from n balls, so nC1. Times 3C1.nC2.2C1.nC1 and divide again by total possibilities, 3nC3 for the answer.
iv) Put the results in a ratio against one another, and use the standard transformation or idk what u call it, Nck=n!/(n-k)!k!, for each part of the ratio. If n is large, n, n-1, n-2 etc, are all around the same value n, so u can write n.n-1.n-2 as n^3 etc. Simplify and u have result.
