Probability and Combinatorics in Prepswift

GRE Quant Problem Solving
1

Hi everyone,

I am confused when to multiply by (total!/repeat!) and when not too. I know for combinatorics order does not matter, so that is why we need to get rid of the repeats. I have attached two screenshots with two problems from prepswift. One needed to multiply by (total!/repeat!) and one not. Can anyone tell me why it is that way for the question not needing to multiply? I am thinking that order does not matter in the question as well.

Your help is greatly appreciated,

Anny

Screenshot (741)
Screenshot (741)1920×1080 103 KB

Screenshot (740)
Screenshot (740)1920×1080 97.3 KB

2

You are right! The order does not matter in the second case as well. They have not multiplied it by (total!/repeat!) because they are considering individual possible cases. You could try using the total!/repeat! formula and you would get the same answer -

P(Passing exactly two tests) = (3/4)^2 * (1/4) * (3!/2!1!) = 27/64

3

Hi,

Great, I see thanks!

~ Anny