Answer to Question #234797 in Statistics and Probability for Dude

Question

A box contains 24 light bulbs, of which four are defective. If a person selects four bulbs from the box at
random, without replacement, what is the probability that all four bulbs will be defective?

Answer 1

Number of ways to select r items from n, $C^n_r = \frac{n!}{(r! \times (n-r)!)}$

Number of bulbs = 24

Number of defective bulbs = 4

Number of working bulbs = 24 - 4 = 20

P(all four bulbs will be defective) = Number of ways to select 4 defective bulbs / Number of ways to select any 4 bulbs

$= \frac{C^4_4 }{ C^{24}_4} \\ = \frac{1}{10626}$