Should I use nPr or nCr?

Question

Hi
I want to calculate "How many combinations of 4 characters out of 62 can be made."
I want to make combinations from a-z, A-Z, and 0-9. I know permutation or combination can be used to calculate it but I am not sure which one to use in this regard. The combinations should be unique for example "a1sZ" is different from "a1Sz" etc.

Answer 1

Don't worry about P or C, think instead about what you are doing.

You have 4 slots, __*__*__*__
The first one can be any of 62 values, the second any of the remaining 61, the third any of the remaining 60, the 4th any of 59:

62*61*60*59.

Each possibility appears exactly once in this count. If the order was not important, then something like aByZ would be on the list 24 times, as aByZ, aBZy, ..., so you would divide by the 4! ways of rearranging them.

Or, if you allowed replacement, the answer would be 62*62*62*62.

As a graduate degree holder in math and a former college math instructor, I always found the best way to approach this type of confusion is by concentrating on the concept rather than the name or the definition

Answer 2

Use nPr...

nPr is when the ordering of the term makes a difference. For example, if THIS is different from TIHS, then use nPr.

nCr is when ordering does not make a difference, just merely the existence. So THIS is the same as TIHS or HITS because they use the same letters, just in different order...

From your question, I think you should use nPr. If a1sZ is different from a1Zs, use nPr. It they are the same, use nCr.

Answer 3

nPr is used when the arrangement of the combinations are important while nCr does not account for arrangement that means to say, "a1sZ" is the same as "a1Sz".
Therefore, for your case you should use nPr since you mentioned that "a1sZ" is different from "a1Sz".