Probability of specific event occurring from list of possible outcomes

Question

There are 7 letters: A, B, C, D, E, F, G. If 3 letters are randomly picked from the list, what is the probability that a specific letter (e.g. G) would come out? What about 2 letters (e.g. A OR B)? What are formulas to solve this problem?

Answer 1

I would think the problem as follows (this is for one letter come out):

step one: you fix on a specific letter come out, say, A. then, the total number of combinations containing A would be the number of combinations of randomly selecting 2 letters out of the other six letters, which is 15.

step two: the total number of combination of three letters being randomly selected is 3 out of 7, which is 35.

so, the probability of a specific letter come out is equal to 15/35=0.4286.