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StatisticsQ&A LibraryPhase I of a Clinical Trial 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 bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.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 14 people are selected from the 16 that are available?b. If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible?c. If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?Question

Asked Jan 23, 2020

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Phase I of a Clinical Trial 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 bexarotene involved only 14 subjects. Assume that we want to treat 14 healthy humans with this new drug and we have 16 suitable volunteers available.

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 14 people are selected from the 16 that are available?

b. If 14 subjects are selected from the 16 that are available, and the 14 selected subjects are all treated at the same time, how many different treatment groups are possible?

c. If 14 subjects are randomly selected and treated at the same time, what is the probability of selecting the 14 youngest subjects?

Step 1

**a. Different sequential arrangements that are possible if 14 people are selected from the 16 that are available:**

Here, *n* is 16 and *r* is 14. The selections are made without replacement.

The different sequential arrangements that are possible if 14 people are selected from the 16 that are available is obtained as **10,461,394,944,000**, from the calculation given below:

Step 2

**b. Different treatment groups possible:**

The different treatment groups possible is obta...

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