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 5 subjects. Assume that we want to treat 5 healthy humans with this new drug and we have 10 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 5 people are selected from the 10 that are available? Choose the correct answer below. A. \( 3,628,800 \) B. 30,240 C. 120 D. 252

To find the number of different sequential arrangements possible when selecting 5 people from 10 available volunteers, we can use the concept of permutations. The number of permutations of selecting 5 people from 10 available volunteers can be calculated using the formula for permutations: \[ P(n, r) = \frac{n!}{(n-r)!} \] where: - \( n \) is the total number of items (10 volunteers in this case), - \( r \) is the number of items to be selected (5 people in this case). Substitute the values into the formula: \[ P(10, 5) = \frac{10!}{(10-5)!} = \frac{10!}{5!} \] Calculate the factorial values and simplify the expression to find the number of different sequential arrangements possible. Simplify the expression by following steps: - step0: Solution: \(\frac{10!}{5!}\) - step1: Expand the expression: \(\frac{10\times 9\times 8\times 7\times 6\times 5!}{5!}\) - step2: Simplify: \(10\times 9\times 8\times 7\times 6\) - step3: Multiply the terms: \(10\times 3024\) - step4: Multiply the numbers: \(30240\) The number of different sequential arrangements possible when selecting 5 people from 10 available volunteers is 30,240. Therefore, the correct answer is: B. 30,240