solve by a method of your choice.
a medical researcher needs 6 people to test the effectiveness of an experimental drug. if 14 people have volunteered for the test, in how many ways can 6 people be selected?
the 6 people can be selected in ways.
(simplify your answer. type a whole number.)

Question

Accepted Answer

# Explanation:
## Step1: Identify the combination formula
The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 14$ (total number of volunteers) and $r=6$ (number of people to be selected).
## Step2: Substitute values into the formula
$$
\begin{align*}
C(14,6)&=\frac{14!}{6!(14 - 6)!}\
&=\frac{14!}{6!×8!}\
&=\frac{14\times13\times12\times11\times10\times9\times8!}{6!×8!}\
&=\frac{14\times13\times12\times11\times10\times9}{6\times5\times4\times3\times2\times1}\
\end{align*}
$$
## Step3: Simplify the expression
$$
\begin{align*}
\frac{14\times13\times12\times11\times10\times9}{6\times5\times4\times3\times2\times1}&=\frac{14\times13\times12\times11\times10\times9}{720}\
&=3003
\end{align*}
$$

# Answer:
$3003$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the combination formula

Step2: Substitute values into the formula

Step3: Simplify the expression

Answer: