Question

a clinical test on humans of a new drug is normally done in three phases. phase 1 is conducted with a relatively small number of healthy volunteers.
for example, a phase 1 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
stable volunteers available. complete parts (a) through (c) below

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? choose the correct answer below
a 51,891,840
b 40,320
c 6,227,020,800
d. 1,287

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?
there are 1287 different treatment groups possible.

c. if 8 subjects are randomly selected and treated at the same time, what is the probability of selecting the 8 youngest subjects?
p(selecting the 8 youngest subjects) = □ (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the combination formula

The number of combinations \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 13\) and \(r=8\). We found in part (b) that \(C(13,8)=\frac{13!}{8!(13 - 8)!}=\frac{13!}{8!×5!}=\frac{13\times12\times11\times10\times9}{5\times4\times3\times2\times1}=1287\).
The probability formula is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The number of favorable outcomes (selecting the 8 youngest subjects) is \(1\).
The total number of outcomes is the number of combinations of selecting 8 subjects out of 13, which is \(C(13,8) = 1287\) (from part (b)).

Step2: Calculate the probability

\(P=\frac{1}{C(13,8)}\)
Substitute \(C(13,8)=1287\) into the formula: \(P=\frac{1}{1287}\)

Answer:

\(\frac{1}{1287}\)