Question

A botanist is studying the effects of water and fertilizer on certain flowering plants. Plants are given 8, 16, or 32 ounces of water each day, and the water that is given contains either a 2%, 5%, or 10% dissolved fertilizer solution.
How many treatments are used in this experiment?

Enter your answer as a number, like this: 42

Answer 1

As botanist is studying the effect of water and fertilizer on certain flowering plants.

Three Distinct amounts of water having different amount of fertilizer contents in them is used for the purpose of Experimentation.

That is, Plants are given 8, 16, or 32 ounces of water each day, and the water that is given contains either a 2%, 5%, or 10% dissolved fertilizer solution.

Number of treatments  used in this experiment taking 8, 16, or 32 ounces of water each day taking two at time= $_{2}^{3}\textrm{P}=6$ that is (8,16),(16,8),(8,32),(32,8),(16,32),(32,16).

So, Number of treatments  used in this experiment taking 8, 16, or 32 ounces of water each day taking all at time =$_{3}^{3}\textrm{P}=6$

that is (8,16,32) , (8,32,16),(16,8,32),(16,32,8),(32,8,16),(32,16,8)

These are the orders in which water is used for flowering the plants that is first day 8 ounces of water, second day 16 ounces of water, third day 32 ounces of water, or first day 8  ounces of water, second day 32 ounces of water, third day 16 ounces of water, ...........

So, there are 6 possible arrangements using (8, 16 and 32 ) ounces of water taking all at a time and 6 possible arrangements using (8, 16 and 32 ) ounces of water taking two at a time.

Or there are total of [6 × 3= 18] + [6 × 2= 12],=30 treatments.