Problems from Combinations without repetition

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: $$C_{30,5}={\displaystyle \frac{30!}{5!(30-5)!}}=142.506$$

Solution:

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

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