Question

When a clinical trial of a new drug in humans is carried out they are generally carried out in three phases. Phase I consists of a small group of healthy volunteers. Assume we want to treat 20 healthy humans with a new drug and we only have 30 volunteers available.

A. If the subjects are selected and treated in sequence, so that the trial is discontinued if someone has an adverse reaction, how many different arrangements can be obtained if 20 people are selected from the 30 that are available?

b. If 20 subjects are selected from the 30 that are available and the 20 selected subjects are treated at the same time, how many different groups of treatments are possible?

Answer 1

(A) They are selected and treated one at a time

The first person can be chosen from the 30 in 30C1 = 30 ways. The second person can be chosen in 29C1 = 29 ways and so on.

Then the number of different arrangements = 30 * 29 * 28 * .....*14 * 13 * 12 * 11 = ³⁰P₂₀ = 7.30966 x 10²⁵.

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(B) When the 20 subjects are chosen from the pool of 30 and treated simultaneously, then the number of arrangements

= ³⁰C₂₀ = 30,045,015

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