General hints on doing combination and permutation problems?

Question

hero · Answer

To do combination and permutation, you need to consider the following:

1. Whether or not order matters
2. Whether or not repetition is allowed

If order matters, then it is a permutation
If order doesn't matter, then it is a combination

If it is a permutation and repetition is allowed, then the relationship between n and r is $$n^r$$

If it is a permutation and repetition is not allowed then the relationship between n and r is $$\frac{n!}{(n - r)!}$$

If it is a combination and repetition is allowed, then the relationship between n and r is $$\frac{n!}{r!(n-r)!}$$

If it is a combination and repetition is not allowed, then the relationship between n and r is

$$\frac{(n + r - 1)!}{r!(n - 1)!}$$