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

Accepted Solution

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.