Answer:
a) 40 possible combinations
b) 8 possible combinations
Step-by-step explanation:
Given:
- Levels of temperature = 4
- Levels of catalysts = 2
- Levels of pressure = 5
Find:
To consider all possible combinations, how many experiments would need to be conducted?
With the three factors noted, how many experiments would need to be run to cover all possible combinations with each of the three factors at two levels?
Solution:
- We experiment each of the 3 factors to a certain level. So to conduct any experiment we have:
Temperature = 4C1 = 4 possibilities
Catalysts = 2C1 = 2 possibilities
Pressure = 5C1 = 5 possibilities.
- Hence, the total outcome for one particular experiment is a combination of all 3 factors possibility:
Total possible outcomes = 4*2*5 = 40 possible combinations
- Similarly if all factors are restricted to two levels only we have:
Temperature = 2C1 = 2 possibilities
Catalysts = 2C1 = 2 possibilities
Pressure = 2C1 = 2 possibilities.
- Hence, the total outcome for one particular experiment is a combination of all 3 factors possibility:
Total possible outcomes = 2*2*2 = 8 possible combinations
= 400 ft^3
