# probability: 20 defective in 500; prob. all 10 defective

#### anasylum

##### New member
A container with 500 devices has 20 defective ones. If the devices are selected together from a container, what's the probability that all 10 are defective?

ok, assuming the equation might looks like this 500!/490!10!, can anyone help? I can cancel out the 490!, and reduce some numbers but I still find what i have left to be too high, anyone with any thoughts?

#### galactus

##### Super Moderator
Staff member
This is a hypergeometric distribution. Like a binomial only without replacement.

Given a population of N items having k successes and N-k failures, the probability of selecting a sample of size n that has x successes and n-x failures is given by:

$$\displaystyle \frac{C(k,x)C(N-k,n-x)}{C(N,n)}$$

Can you finish using the formula?.

#### anasylum

##### New member
Hi,
Not sure yet. What would the C represent?

#### galactus

##### Super Moderator
Staff member
You're not familiar with combinations?. That just the notation for combinations. How many ways to choose k items from n items when order does not matter is C(n,k).

#### anasylum

##### New member
Hi, I am somewhat familiar with combinations and permutations, but this questions is stumping me. Sorry, brain dead here. I'm simply at a loss. Thanks for providing the formula, I just can't work it, but I will keep trying.

All the best,

#### galactus

##### Super Moderator
Staff member
Well, you have N=500 and there are 20 defects in that 500. That means 480 are good.

You are drawing 10 from the 500 and finding the probability that all of those are defects. So, you are choosing 0 of the 480 good ones and 10 of the 20 bad ones. Intuitively, I would say the probability is mighty low.

So, you have(from the formula):

$$\displaystyle \frac{C(480,0)C(20,10)}{C(500,10)}$$