Permutation and combination help needed.

[r_walid]

Hi guys,
I am in a need for someone to explain to me when to use permutation, combination, and when to simply multiply events together.

for example, some problems' solution requires that we multiply the number of possibilities together ("if there are 3 diff. drinks and 7 diff pizza, how many different combinations can a kid pick if he will pick one of each?" the answer is simply 7*3).
but then there are problems that require permutation or combination. When do we use them and why?
and then there are problems where we need to divide 2 combinations together like the problem below:

From a bag containing 4 white and 5 black balls a man draws three at random what is the probability of these being all black. Answer is 5C3 / 9C3

why is it the case in this latter example? why is it just not a simple combination problem? why do we need to divide 2 combinations ?
Thanks for your help.

[welcome]

Please read this doc. I hope it will help.

[r_walid]

Thanks but the document didn't help me much. for example, it didn't dweel deep into the permutation and combination but rather mentions it in the last paragraph with 1 example or 2. I was hoping to find something much more detailed.
I'm hoping if someone can help me figure out the last problem i stated in my original post above regarding the division of the 2 combinations.

Thank you

[aroon7]

for the second problem, there is a simpler way

P(first ball is black)* P(second ball is black)*P(thrid ball is black)

= (5/9)(4/8)(3/7) = 15/126