Question

A warehouse contains ten printing machines, four of which are defective. A company selects five of the machines at random, thinking all are in working condition. What is the probability that all five of the machines are nondefective?

Answer 1

The total number of possible outcomes is the number of ways we can choose 5 machines of 10.

Favorable outcomes are when we choose 5 of 6 non-defective machines.

$P=\cfrac{\begin{pmatrix}6 \\5\end{pmatrix} }{\begin{pmatrix}10\\5\end{pmatrix}}=\\ =\cfrac{6!} {1!\cdot5!} \cdot\cfrac{5!\cdot5!} {10!}=\\ =\cfrac{6!\cdot5! } {10!} =\cfrac{1} {42} .$