Question

An article describes a study in which a new type of ointment was applied to forearms of volunteers to study the rates of absorption into the skin. Eight locations on the forearm were designated for ointment application. The new ointment was applied to five locations, and a control was applied to the other 3. How many different choices were there for the five locations to apply the new ointment

Answer 1

There were 56 different choices for the five locations to apply the new ointment.

Explanation:

The order of the locations in which the new ointment was applied 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 choices were there for the five locations to apply the new ointment

Five locations from a set of 8. So

`C_(8,5) = (8!)/(5!(8-5)!) = 56`

There were 56 different choices for the five locations to apply the new ointment.