Question

solve by a method of your choice.
a medical researcher needs 9 people to test the effectiveness of an experimental drug. if 14 people have volunteered for the test, in how many ways can 9 people be selected?
the 9 people can be selected in \\(\square\\) ways.
(simplify your answer. type a whole number.)

Explanation:

Step1: Use combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 14\) (total number of volunteers) and \(r=9\) (number of people to be selected).

Step2: Calculate factorial values

\(n!=14! = 14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\), \(r!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1\), \((n - r)!=(14 - 9)!=5! = 5\times4\times3\times2\times1\)

Step3: Substitute into the formula

$$
LATEXBLOCK0
$$

Step4: Simplify the expression

$$
LATEXBLOCK1
$$

Answer:

\(2002\)