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 12 suitable 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 12 that are available? choose the correct answer below.
a. 40,320
b. 479,001,600
c. 19,958,400
d. 495

Explanation:

Step1: Identify the permutation formula

The number of permutations of $n$ objects taken $r$ at a time is given by $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 12$ (total volunteers) and $r=8$ (number of people to be selected).

Step2: Calculate the factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $P(12,8)=\frac{12!}{(12 - 8)!}=\frac{12!}{4!}$.
$12! = 12\times11\times10\times9\times8\times7\times6\times5\times4!$. Then $\frac{12!}{4!}=12\times11\times10\times9\times8\times7\times6\times5$.
$12\times11 = 132$, $132\times10=1320$, $1320\times9 = 11880$, $11880\times8=95040$, $95040\times7 = 665280$, $665280\times6=3991680$, $3991680\times5 = 19958400$.

Answer:

C. 19,958,400