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 four locations, and a control was applied to the other four. How many different choices were there for the four locations to apply the new ointment

Answer 1

There were 70 choices for the four locations to apply the new ointment

Explanation:

The order in which the locations 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 choices were there for the four locations to apply the new ointment

Four locations from a set of 8. So

`C_(8,4) = (8!)/(4!(8-4)!) = 70`

There were 70 choices for the four locations to apply the new ointment