 #1
 101
 11
Summary:

In a bowl you got 3 white and 4 black marbles.
Pick 2 at random without putting back the marble you picked.
What's the probability of you picking one white and one black marble?
My approach is the amount of successfull options / total amount of options.
I can first pick white in 3 different ways. Then black in 4 different ways
3 * 4
But I can also pick black first then white
4 * 3
Total amount of ways to pick marbles are
7 *6
So the probability is:
(3*4 + 4 * 3) / (7 * 6) = 4/7
which is correct.
But my question is, how do I know how many ways I could've picked successfull options?
In this case it¨'s obvious that I can pick 3 * 4 and 4 * 3 only, but if I have more colored marbles to pick from etc. What's the formula for that?
I don't see how it could be combinations, 7 Choose 2? or 4 Choose 1? Maybe it's binominal 2 over 1 but what does that even mean?
I can first pick white in 3 different ways. Then black in 4 different ways
3 * 4
But I can also pick black first then white
4 * 3
Total amount of ways to pick marbles are
7 *6
So the probability is:
(3*4 + 4 * 3) / (7 * 6) = 4/7
which is correct.
But my question is, how do I know how many ways I could've picked successfull options?
In this case it¨'s obvious that I can pick 3 * 4 and 4 * 3 only, but if I have more colored marbles to pick from etc. What's the formula for that?
I don't see how it could be combinations, 7 Choose 2? or 4 Choose 1? Maybe it's binominal 2 over 1 but what does that even mean?