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Apply Counting Principle to Compute Combinations and Permutations

There are 5 students who work in a bookshop. If the bookshop needs 3 people to operate, how many days straight could the bookshop operate without the same group of students working twice?

Combinations of $n$ objects taken $r$ at a time:

The number of combinations of $r$ objects taken from a group of $n$ distinct objects is denoted by $nCr$ and is given by the formula: $nCr=\frac{n!}{(n-r)!r!}$

$n=5$

$r=3$

$5C_{3}=\frac{5!}{(5-3)!3!}$

$5C_{3}=\frac{5\times4\times3\times2\times1}{(2\times1)(3\times2\times1)}=\frac{5\times4}{2\times1}=10$

10 days