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nlexa [21]
3 years ago
9

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

Mathematics
1 answer:
coldgirl [10]3 years ago
5 0

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 <em>combinations</em>.

Combinations take into account different ways to choose elements from a group when <em>order </em>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 <em>order</em> is <em>irrelevant</em> here to calculate the different groups.

Combinations can be calculated using this formula:

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

Where <em>n</em> is the total of members of the consumer group: 30,  and <em>k</em> 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.

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