Answer :
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:
[tex]\frac{n!}{(n-k)! k!}[/tex]
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:
[tex]n! = n * (n-1) * (n-2) * (n-3) ... 3 * 2 * 1[/tex]
Then,
[tex]\frac{30!}{(30-3)! 3!} = \frac{30*29*28*27!}{27! 3!}[/tex]
where
[tex]\frac{27!}{27!} = 1 [/tex] (as a way to simplify terms easily)
So,
[tex]\frac{30*29*28}{3*2*1} = \frac{30}{3}*29*\frac{28}{2}[/tex]
And finally,
[tex]10*29*14 = 4060[/tex] .
It is always recommendable to simplify as much as possible all terms involved to have an easier calculation and get the correct answer.