Question

a box contains 25 transistors, 6 of which are defective. If 6 are selected at random, find the probability that a) all are defective. b) none are defective

Answer 1

Let's say you pick the transistors one at a time.
On the first pick, what is the probability of picking one defective transistor?
6/25
On the second pick, what is the probability of picking one defective transistor?
5/24
Etc.
The probability of picking 6 defective ones is
6/25 * 5/24 * 4/23 * 3/22 * 2/21 * 1/20

Now do a similar thing for picking no defective transistors.