Question about Using the Formula for Combinations in Probability

[Shoney45]

Homework Statement

Each of 12 refrigerators of a certain type has been returned to a distributo because of the presence of a high pitched oscillating noise. Suppose that 5 of these 12 have defective compressors and the other 7 have less serious problems. If they are examined in random order, let X = the number among the first 6 examined that have a defective compressor. Compute the following:

P(x = 1)

E(X)

E(X^2)

Homework Equations

(n choose k) = n!/k!(n-k)!

The Attempt at a Solution

My random sample is 6, and there are 12 choose from. But I cant' seem to come up with a combination that makes any sense. (I'm just speaking specifically about trying to find P(x=1)

 

[Dick]

To get one bad compressor in a sample of 6, you have to choose 1 from the group of 5 that have bad compressors and 5 from the group of 7 that don't. Then to get the probability you divide by the number of ways to choose 6 from the 12 sample total. How do you express that in combinations language?

 

[Dick]

Duplicate of https://www.physicsforums.com/showthread.php?p=2628312#post2628312