Question

A carton of 18 rechargeable batteries contains one that is defective. In how many ways can an inspector choose 4 of the batteries and get the defective battery?

Answer 1

Given, a carton of 18 rechargable batteries has exactly one defective item.

The inspector wishes to choose 4 of the batteries.

To count the cases where the sample of 4 batteries has the defective one, we note that the sample has to contain the battery which is defective and the remaining 3 batteries can be any 3 from the 17 non defective ones.

So the number of ways is :

                                                 $=\binom{17}{3}*\binom{1}{1}$

                                                 $=\binom{17}{3}$

                                                 $=17! /(3! * 14!)$

                                                  $=680$      ways