Question

A medical research group plans to select 2 volunteers out of 8 for a drug experiment. In how many ways can they choose the 2 volunteers?

Answer 1

Answer:

They can choose the 2 volunteers in 28 different ways

Step-by-step explanation:

Well, as the research group has to choose 2 volunteers out of 8, this means that it doesn't matter the order in which they choose them as long as they are two.

In statistics this is considered a counting technique and is called combination.

The combination formula is:

$C(n,r)=\frac{n!}{r!(n-r)!}$

where

$n$ is the set of elements

and

$r$ is the number of elements taken from n

Then $n=8$ and $r= 2$

We replace in the combination formula:

$C(8,2)=\frac{8!}{2!(8-2)!}$

$C(8,2)=\frac{8!}{2!(6!)}$

$C(8,2)=\frac{40320}{2(720)}$

$C(8,2)=\frac{40320}{1440}$

$C(8,2)=28}$

This result means that Medical research group can choose the 2 volunteers in 28 different ways