1. ## Small combinatorics question

Hey all! I was hoping you could help me get a 'second opinion' to a problem I ran into. It's most likely one of the most basic combinatorics question one can run into but I'm notoriously awful at it.
Here goes:

There are 8 tops in a closet. 3 red ones by the sizes of S,M and L; 3 blue ones, sizing S,M and L again, and 2 white ones, which are M and L.
2 tops are chosen randomly.
What's the probability that the chosen tops will not be white or/and small? *clarification: We need 2 shirts to be a combination of blue/red/medium/large.

I tried to solve this using combinatorics as well as conditional probability, both led me to different answers.

using combinatorics, I did-
[(2 out of 3)+(2 out of 3)+(1 out of 3)*(1 out of 3)]/(2 out of 8)
meaning we either select 2 shirts out of the 3 red OR 1 out of the red, 1 out of the blue, OR 2 out of the 3 blue ones.

My husband thought we should do it this way:
[(6 out of 8)*(4 out of 6)+(5 out of 7)*(3 out of 5)]\(2 out of 8)
so- we choose total 6 out of the 8 tops, (3 blue, 3 red), time it by the selection of sizes we want, and we repeat this picking the second top.
His end result was >1 however.

I tried using conditional probability too, and basically did (3/8*1/3)*2

2. ## Re: Small combinatorics question

(4 choose 2) / (8 choose 2) = 3/14

or

(4/8)*(3/7) = 3/14

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