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?
We start by finding the total number of draws that you can do:
6 * 5 * 4 * 3 * 2 * 1
Now, we have to find the probability that you actually draw your pair:
6 * 1
-> For the first pair:
4 * 1
-> After taking out the second pair:
2 * 1
-> For the third pair
So, successes are: (6 * 4 * 2)/(6 * 5 * 4 * 3 * 2 * 1)
1/(5 * 3)
So the probability is 1/15.
I might be incorrect as I'm not the best at this, so if you find it incorrect please tell me.