Here's my question.
I have $6$ gold coins, $4$ silver coins and $3$ bronze coins in my pocket. I take out three coins at random. What is the probability that they are all of different material?
I had thought that the answer was $\frac{1}{13 \choose 3}$. However, the answer turned out to be $\frac{72}{13 \choose 3}$. Why?
Isn't there only one combination of 3 coins that allows for the coins to be different?