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 7 subjects. Assume that we want to treat 7 healthy humans with this new drug and we have 11 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 arrangement are possible if 7 people are selected from the 9 that are available? Choose the correct answer below. A. 181,440 B. 362,880 C. 5,040 D. 36b. If 7 subjects are selected from the 9 that are available, and the 7 selected subjects are all treated at the same time, how many different treatment groups are possible? There are_________ different treatment groups possible c. If 7 subjects are randomly selected and treated at the same time, what is the probability of selecting the 7 youngest subjects? P(selecting the 7 youngest subjects)_________(Type an integer or a simplified fraction. )

Answer 1

The number of sequential arrangements if 7 people are selected from 9 is 181,440. If all 7 selected subjects are treated at the same time, there is only one treatment group. The probability of selecting the 7 youngest subjects cannot be calculated without additional information.

Step-by-step explanation:

In order to calculate the number of different sequential arrangements if 7 people are selected from the 9 available, we can use the permutation formula:
P(n,r) = n! / (n-r)!
where n is the total number of people and r is the number of people being selected.
So, for this question, we have n = 9 and r = 7.
Plugging these values into the formula, we get:
P(9,7) = 9! / (9-7)! = 9! / 2! = (9 * 8 * 7 * 6 * 5 * 4 * 3) / (2 * 1) = 181,440

Therefore, the answer to part (a) is A. 181,440.

In part (b), if the 7 selected subjects are all treated at the same time, then there is only one treatment group because all subjects receive the same treatment.
Therefore, the answer to part (b) is 1.

Finally, in part (c), if 7 subjects are randomly selected and treated at the same time, the probability of selecting the 7 youngest subjects would depend on the total number of subjects available and their ages.
Without additional information about the ages of the subjects, we cannot calculate the exact probability.
Therefore, the answer to part (c) is undefined.