1. nCr or nPr?

I'm reading my textbook, but i don't understand the difference between $\displaystyle ^n\mathrm{C}_r$ and $\displaystyle ^n\mathrm{P}_r$? All it says that for $\displaystyle ^n\mathrm{P}_r$ the order matters and for $\displaystyle ^n\mathrm{C}_r$,the order doesn't matter but i'm not sure what this means. I can do the working out etc. but I'm just worried when i come across a worded problem, i'm not sure which one to apply?

if anyone can explain, il be super grateful!

2. Well, it exactly is as your textbook says: Does order matter or not?

If you get a question about differently coloured cars arranged in different ways, order matters. Ways of seating people is another common one. Therefore, for both you use $\displaystyle ^n\mathrm{P}_r$
Combinations are used when order does not matter. In how many different ways can you choose a committee consisting of 3 people from 25 students?$\displaystyle ^{25}\mathrm{C}_3$

Does this make it any clearer?

3. Originally Posted by chinkmeista
I'm reading my textbook, but i don't understand the difference between $\displaystyle ^n\mathrm{C}_r$ and $\displaystyle ^n\mathrm{P}_r$? All it says that for $\displaystyle ^n\mathrm{P}_r$ the order matters and for $\displaystyle ^n\mathrm{C}_r$,the order doesn't matter but i'm not sure what this means. I can do the working out etc. but I'm just worried when i come across a worded problem, i'm not sure which one to apply?

if anyone can explain, il be super grateful!
Hi chinkmeista,

Here is an example:

We need to choose 3 officers out of 8 members in an organization (perhaps to share the work load together). How many ways can we do this?

This is going to be a problem using combination since we are picking 3 while there is no difference which person get pick first, since 3 positions are the same. (Order does not matter)

Thus there is $\displaystyle ^8\mathrm{C}_3$ ways.

On the other hand, if the problem is instead:
We need to choose 3 officers out of 8 members, a president, a secretary, and a treasurer, in an organization. How many ways can we do this?

This is going to be a problem using permutation since we are picking 3 while there is a difference which person is the president, or the secretary, and so forth. (Order does matter)

Thus there is $\displaystyle ^8\mathrm{P}_3$ ways.

Does this make sense?

4. Yeah a little bit thanks, just have to try my best to understand the wording of the question!