Probability Question check

A bag contains 5 blue marbles, 4 white marbles, and 3 red marbles. If three marbles are randomly selected from the bag, what is the probability that the marbles selected will be of the same color? Express your answer as a common fraction.

In the future I will need a lot of your guy's help to check my answers, as the math competitions are starting soon! and i need to prepare

Also the confirming if I am a robot thing is SUPER annoying. Make it where once you passed the test ONCE, you don't need to do it again if you have an account.

How I did it:
 

5 + 4 + 3 = 12 total number of marbles

that means 12 choose 3 = 220 ways to choose 3 marbles

Now the question asks how many ways will the marbles be the same color

So for red

there is only 1 way

For White,

there is 4 ways of choosing 3 out of 4

And for blue 

there is 10 ways of choosing 3 out of 5

So is 1 + 4 + 10 = 15 ways you can pick three marbles of the same color

So 15/220 = 3/44