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?
See development and solution
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.