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

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joaobezerra joaobezerra · Answer 1 · 2021-03-14T01:56:22+01:00

Answer:

There were 28 different choices for the six locations to apply the new ointment

Step-by-step explanation:

The order in which the location are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Two events, A and B are independent, if:

[tex]P(A \cap B) = P(A)P(B)[/tex]

How many different choices were there for the six locations to apply the new ointment?

Six locations from a set of 8. So

[tex]C_{8,6} = \frac{8!}{6!2!} = 28[/tex]

There were 28 different choices for the six locations to apply the new ointment