Five people have applied for three different positions in a store. If each person is qualified for each position, in how many ways can the positions be filled?
Can someone tell me if I have to use permutations $\mathrm P(5, 3)$ or combinations $\mathrm C(5, 3)$ and why?
Thanks for any help!
Best Answer
Well, consider the positions available. There are three. They literally told you that they are different. So consider positions one two and three.
You have five candidates. You fill the first position and there are 5 ways to do it.
Then you consider the second position. You already hired one person, so there are 4 people left. Hence, there are four ways to fill position two.
Lastly, there are 3 ways to fill spot three.
Hence, there are $5\cdot 4\cdot 3$ ways to fill the positions.
Secretly, we used permutations. There are are 3 positions that are different and hence "the order matters". There are five candidates. Hence ${_5\mathsf P}_3$.