Question

A clinical test on humans of a new drug is normally done in three phases. Phase I is conducted with a relatively small number of healthy volunteers. For​ example, a phase I test of a specific drug involved only 8 subjects. Assume that we want to treat 8 healthy humans with this new drug and we have 13 suitable volunteers available. Complete parts​ (a) through​ (c).

a. If the subjects are selected and treated in​ sequence, so that the trial is discontinued if anyone displays adverse​ effects, how many different sequential arrangements are possible if 8 people are selected from the 13 that are​ available?

b. If 8 subjects are selected from the 13 that are​ available, and the 8 selected subjects are all treated at the same​ time, how many different treatment groups are​ possible?

c. If 8 subjects are randomly selected and treated at the same​ time, what is the probability of selecting the 8 youngest​ subjects?

Answer 1

(a)

Here order of subjects are important.

First subject can be selected in 13 ways, second in 12 ways, third in 11 ways and so on. So possible number of sequences of 8 people is

(b)

Here order of people is not important so combination will be used. Number of ways of selecting 8 people out of 13 is

(c)

Out of 1287 possible selections only one has 8 youngest people so the probability of selecting the 8 youngest​ subjects is

P = 1 /1287 = 0.000777