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