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Math - probability

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A lab is developing a new medication for headaches. To do so,they must choose from 10 active ingredients, 5 preservatives and 2 presentations (capsules or tablets). A tablet or a capsule must have at least one active ingredient and one preservative.

a)How many different medications with one active ingredient and two preser-
vatives can the lab produce?

b)How many different medications with two active ingredients and one
preservative can the lab produce?

c)How many different medications with one active ingredient and at most
two preservatives can the lab produce?


For a) there are 10 choices for the active ingred., and 5C2 (5 choose 2) ways to select the preservative, times the number of presentations. Now use the multiplication rule.
For b) there are 10C2 ingred., and 5C2 preserv. times the number of presentations.
For c) there are 10C1 ways to select the ingredient, 5C1 + 5C2 ways for the preserv, and 2 presentations.

Note: nCm means n choose m.

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