Problems from Combinations without repetition

In a class with $$30$$ pupils, $$5$$ volunteers have to go out to do an activity. How many groups of $$5$$ different volunteers can there be?

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Development:

In this case, $$n=30$$ (because there are $$30$$ pupils) and $$k=5$$ (since it is necessary to form a group of $$5$$ people).

Also the order does not matter and the people cannot repeat themselves. Therefore it is a question of a combination of $$30$$ elements taken $$5$$ at a time, that is to say: $$$C_{30,5}=\dfrac{30!}{5!(30-5)!}=142.506$$$

Solution:

There are $$142.506$$ groups of $$5$$ possible volunteers.

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