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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?
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: $$C_{30,5}=\dfrac{30!}{5!(30-5)!}=142.506$$
There are $142.506$ groups of $5$ possible volunteers.