CAA: Christian Anime Alliance

I'm having a problem with a math word problem in my book and I was wondering if someone could help me with it.

Problem is as follows:
"A distrubution center receives shipments of a product from three different factories in the following quantities: 50, 35, and 25. Three times a product is selected at random, each time without a replacement. find the probability that all three products came from the third factory."

The problem deals with probability and the answer in the back of the book is ".011". However, I'm unsure on the process of the problem and would like someone to help me out with that.

Thanks.

I'll give it a shot. Someone else might be able to explain it better than I can(or provide a faster method).

First find the total number of choices: 50+35+25=110

Then find the probability of each selection. The first time there is a 25/110 chance of recieving a package from factory three. For the second choice, there is only a 24/109 chance, since one package from factory three was already removed. The third choice has a 23/108 chance of factory three.

Since you want all three to happen(choice1 AND choice2 AND choice3) you multiply the three together.

(25/110)*(24/109)*(23/108) which come out around .01065 something.

Ah that helped.

What I was getting confused on was the "50, 35, and 25" part. I didn't know that each was from the three different factories. I looked at it as each factory having 50, 35, and 25. So sorta like like a matrix.

[50,35,25]
[50,35,25]
[50,35,25]

Then instead of using the numbers, the problem asks for the packages and from one factory...

The way I look at problems messes me up royally. lol ^-^ Thanks for the help.