Question

Suppose that four microchips in a production run of sixty are defective. A sample of six is to be selected to be checked for defects. (a) How many different samples can be chosen

Answer 1

50,063,860 different samples can be chosen

Explanation:

The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

How many different samples can be chosen

We choose 6 microchips from a set of 60. So

`C_(60,6) = (60!)/(6!(60-6)!) = 50063860`

50,063,860 different samples can be chosen