Answer to Question #290808 in Statistics and Probability for jack

Question

A box contains 18 light bulbs. Of these, four are defective. Five bulbs are chosen at random. What is the probability that four are defectives?

Answer 1

We have the total of 18bulbs

14 are good and 4 are defectives.

Total number of outcome is $\binom{18}{5}\\$

Selecting 1 good bulb from 14 is $\binom{14}{1}$

Selecting 4 defectives bulb from 4 is $\binom{4}{4}\\$

Then the solution is

$\frac{\binom{14}{1}\times\binom{4}{4}}{\binom{18}{5}}=\frac{14 \times 1}{8568}=0.0016$