Question

1. A chemist is studying the effects of temperature, pressure, and type of catalyst on a chemical reaction. The chemist can set the temperature to one of 3 different levels, the pressure to 4 different levels, and can choose among 5 catalysts. How many possible experiments can be conducted in which either the lowest temperature or one of the two lowest pressures are used? [Note that this includes the cases in which the lowest temperature and one of the two lowest pressures are used together.]

Answer 1

This is a case of multiplication rule to find the total number of ways. This is computed here as:

= Total number of different temperature levels * Total number of different pressure levels * Total number of catalysts

= 3*4*5

= 60

But these are the total number of ways.

Now possible the experiments that can be conducted in which either the lowest temperature or one of the two lowest pressures are used is computed here as:

= Total number of ways - Total number of ways in which the lowest temperature is not used and one of the two lowest pressures are also not used

= 60 - (3 - 1)*(4 - 2)*5

= 60 - 2*2*5

= 60 - 20 = 40

Therefore there are a total of 40 ways to conduct the experiment here.