Question

the effects of te An pressures, and six 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? is ure, pressure, and type of catalyst on yield from a certain chemical reaction. Five different t 90 (b) How many experimental runs are there that involve use of the lowest temperature and two lowest pressures? 12 (c) Suppose that six different experimental runs are to be made on the first day of experimentation. If the six are randomly selected from among all the any group of six has the same probability of selection, what is the probability that a different catalyst is used on each run? (Round your answer to four 0 0154 decimal places.) Need Help? Read it

Answer 1

(a)

Number of possible experimental runs = 5 * 3 * 6 = 90

(b)

If there are only one level of temperatures and two levels of pressure, then

Number of possible experimental runs = 1 * 2 * 6 = 12

(c)

Number of ways to select group pf six experiments out of 90 = ⁹⁰C₆ = 90! / (90 - 6)! * 6!

= (90 * 89 * 88 * 87 * 86 * 85) / (6 * 5 * 4 * 3 * 2 * 1) = 622614630

For a fixed catalyst, number of possible experimental runs = 5 * 3 = 15

So, number of ways to select group of six experiments with all different catalysts = Number of ways to select 6 catalyst from 6 groups of 15 experimental runs = 15⁶

Probability that all selected group of six experiments have different catalysts = 15⁶ / 622614630

= 0.0183