I think I understood. I mean I can place the logic in my head now. Let's see if I got this right.

In a bag with 10 white marbles and 3 red marbles I take 7 without replacement:

Finding the probabilities of getting 1 red marble means comparing the number of ways I can obtain exactly 1 red marble and 6 white marbles (desirable outcome) when drawing 7 marbles to all possible outcomes when drawing 7 marbles.

A. First I calculate the number of all possible combinations when taking 7 out of 13.

[texto ]{13\choose7} \,=[/tex] (13!)/(7!)(13-7)!= 1,716 possible combinations

Then I calculate the number of ways I can obtain my desirable outcome of 1 red and 6 white, which is the number of combinations for obtaining 1 red out of 3 multiplied by the number of combinations for 6 out of 10 white.

((3!)/(1!)(3-1)!)*((10!)/(6!)(10-6)!) = (3)(210) = 630 ways of obtaining the desirable outcome

Then I calculate P which is

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B. To find the probability of 2 reds marbles we have:

Yeah, thanks again everybody, I was confused about the notion of 'number of ways' which is actually only the number of combinations for a particular outcome.