How many doses?

Question

There are 16 capsules.

4 capsules contain 2.5 mg

4 capsules contain 5.0 mg

4 capsules contain 7.5 mg

4 capsules contain 10 mg

How many doses are there if you use all capsules in various combinations.

A dose is one or more capsules. If you took all 4 2.5mg capsules at once, that is one dose.

Answer 1

I think I finally figured out the question, Arthur.  There are four different pills and four of each kind of pill.  A "dose" consists of taking one or more pills in any combination.  So since there are five ways to take each type of pill (0, 1, 2, 3, or all 4) and there are four of each type, the number of different combinations would be 5⁴.  But since one of the combinations is 0 of each type, the actual number of doses would be 625 - 1, or 624 doses.

Answer 2

So, you have 4 of each, so there are 16 one-capsule dose.

 

Since there are 16 total capsules, you have 16/2 = 8 two-capsule doses.

 

16/3 = 5 1/3, so that's 5 three-capsule doses.

 

16/4 = 4 four- capsule doses.

 

16/5 = 3 1/5, so three there.

 

16/6 = 2 4/6, so there's two.

 

16/7 = 2 2/7, so two

 

16/8 = 2

 

16/9 = 1 7/9, so one

 

The rest will all give you one, that's 10,11,12,13,14,15,16 for a total of 7 ways.

 

16 + 8 + 5 + 4 + 3 + 2+ 2 + 2 + 1 + 7 = 50 ways to take a dose.