Q:

Need a direction to solve this probability question

50 balls in a bag, 7 of them are white,the others black,
we take out 10 balls, what is the probability that exactly 2 of them are white.
I was thinking i need first to choose the 10 balls so (50 choose 10),
then i have 7/50   * 6/50 for 2 for 2 white balls * (10 choose 2) for placement?
this is really confusing

A:

Your universe ♧=" combination of $10$ balls from $50$ balls". So the cardinal of ♧ is:
$$|♧|=C(10,50)$$
Let's name your event by $A$. So $A=$" 2 Of the 10 balls must be white". The cardinal of $A$ is:
 $$|A|= C(2,7)*C(8,43)$$
For that, we need to choose $2$ white balls from $7$ balls and $10-2=8$ balls from $50-7=43$ balls 
$$P (A)=\frac{\text{ cardinal of the event} A}{\text{cardinal of the universe}} \\
P (A)=\frac{ |A| }{|♧|}\\= \frac{C(2,7)*C(8,43)}{C(10,50)}$$
NB: $C(k,n)$ is the combination of $k$ from $n$. 

