Question

A consumer group has 30 members. In how many ways can the group choose 3 members to attend a national meeting?

Answer 1

Answer:

There are 4060 ways to choose 3 members from the 30 ones to attend the national meeting.

Step-by-step explanation:

It is a question about combinations.

Combinations take into account different ways to choose elements from a group when order is not important. The people is asked to be part of a kind of commitee, that is, no one has a more relevant role that other, so order is irrelevant here to calculate the different groups.

Combinations can be calculated using this formula:

$\frac{n!}{(n-k)! k!}$

Where n is the total of members of the consumer group: 30,  and k is the number of members to be choosen to attend that national meeting.

It is crucial to remember what the factorial notation means:

$n! = n * (n-1) * (n-2) * (n-3) ... 3 * 2 * 1$

Then,

$\frac{30!}{(30-3)! 3!} = \frac{30*29*28*27!}{27! 3!}$

where  

$\frac{27!}{27!} = 1$ (as a way to simplify terms easily)

So,  

$\frac{30*29*28}{3*2*1} = \frac{30}{3}*29*\frac{28}{2}$

And finally,

$10*29*14 = 4060$ .

It is always recommendable to simplify as much as possible all terms involved to have an easier calculation and get the correct answer.