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# Probability

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can u help here

My sock drawer contains two red socks, two white socks, and two blue socks.  For three days in a row, I pull out two socks out of my sock drawer at random.  What is the probability that I get matching socks on all three days?

Feb 10, 2023

#1
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First calculate all the possible cases which is $$\frac{6!}{2!2!2!}$$= 90

Then calculate all the possible cases which this condition occurs. The first time you pull there is three possible ways to pull a matching pair, 3*1, The second time you pull there is 2 possible ways to get a matching pair, 2*!, after you do this, you have to pull a matching pair. So (3*2)/90 = 1/15

You could also do this with choose, (3/(6 choose 2))*(2/4 choose 2) * (1/2 choose 2) which also gives 1/15

Feb 10, 2023