Maths/Probability help

I really need help on this question i have:
you have 6 marbles in a bag and you draw 2 at a time there are 3 red, 2 blue and 1 yellow what is the theoretical probability of each colour combination? eg. RED,YELLOW=

YB: 2 *1/6 *2/5 = 2/15
YR: 2 *1/6 *3/5 = 3/15
RB: 2 *3/6 *2/5 = 6/15
RR: 3/6 *2/5 = 3/15
BB: 2/6 *1/5 = 1/15
........ total ..... 15/15 = 1

note:
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1. note that whenever 2 different colors are there, you need to multiply by 2 because, eg yellow & blue could be YB or BY.
2. the fractions have been putunder a common denominator so that it is easy to check that they add up to 1.

well im not sure if this is what its looking for

but for
red: there are 3 red marbles in a bag of 6 marbles total..... so 3/6 is 50%
blue: there are 2 blue marbles in a bag of 6 marbles total...... so 2/6 is 33.33%
yellow there are 1 yellow marbles in a bag of 6 marbles total...so 1/6 is 16.66%

if it were Red, Yellow..... there were initially 3 out of 6 change.. so you have a 50% chance
to get yellow a second time.. there is a 2/5 chance... 40%..... so .5*.4= .2 so 20% chance

RB = (1/2)(2/5) = 1/5

RY = (1/2)(1/5) = 1/10

BY = (1/3)(1/5) = 1/15