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 three. How many different choices were there for the five locations to apply the new ointment?

Question

Mathematics

Austin Hodge

25 May, 14:39

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 three. How many different choices were there for the five locations to apply the new ointment?

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Colby Krueger · Answer 1

6720 different choices

Step-by-step explanation:

The ointment is put on 5 locations out of 8 locations. There are no markings or anything to differ in the 5 locations, so we can say that the order is not important. Since the order is not important we will use combination, not permutation. The other 3 locations are used for control, so it won't add to the number of possible ways.

The number of ways to put ointment in 5 of 8 locations will be:

8C5 = 8! / (8-5) ! = 6720 ways.