Can you help me with this statistics/Probability problem?

Question

A foundry ships 20 engine blocks of which 5 are defective. A purchaser slects 3 blocks at random off the truck. the shipment will be accepted if no flaws are found. What is the probability the shipment is accepted?

This is not my homework or anything, I am studying for a final and do not know how to do this problem which is on my review sheet. Any help would be great! I think it has something to do with combinations or permutations..?
Thanks!

Answer 1

There are a couple of ways you can do this.

The first is to ask "How many ways are there to choose five of the 15 good engines?" This uses combinations:

15!/[5!*10!] = 3003

Then ask "How many ways are there to choose five of the 20 engines?"

20!/[5!*15!] = 15504

Then divide one by the other -- 19.369%

The other way to do it is to ask the following questions and multiply the probabilities together:

What is the probability of picking a good engine from 20:

15/20

What is the probability of picking another good one:

14/19

Then another & another

13/18, 12/17, 11/16

Multiuply these probabilities together & you get the same answer.

Answer 2

The probability the shipment is accepted is the probability that all 3 selected blocks are normal. Fifteen out of the 20 blocks are normal for the first selection. For the second selection, 14 of the remaining 19 blocks are normal, assuming a normal one was selected the first time. For the third, 13 of the remaining 18 are normal. Since you need to know the probability of all three happening, you multiply these three events.

P(accepted) = (15/20) x (14/19) x (13/18)
= 0.399 (approximated)