Solution to Exercise 2.36.

  Problem Statement: An experimenter is studying the effects of temperature, pressure, and type of catalyst on yield fiom a ertain chemical reaction. Three different temperatures, four different pressures, and five different catalysts are under consideration.

(a) If any particular experimental run involves the use of a single temperature, pressure, and catalyst, how many experimental runs are possible?

Solution: Applying the Product rule for three-tuples, the answer is

$$3 \times 4 \times 5 \; = \; 60.$$

(b) How many experimental runs are there that involve use of the lowest temperature and two lowest pressures?

Solution: Again we may apply the product rule, giving

$$1 \times 2 \times 5 \; = \; 10 .$$