when to use nPr or nCr?

you use nPr, when you want to take note of the order.

Example, in choosing between A,B,C,D & E , how many ways can you choose any 3 arranged letters. (This means ABC is different from ACB or BCA or...)

Then 5P3.

you use nCr , when the order is not important.

Example , how many ways can you get three letters from A,B,C,D & E. (here ABC is no different from BAC since you just got A&B&C.)

Then 5C3.

d:

Npr And Ncr

nPr is when order matters

nCr is when order does not matter

lets take the lottery

if we are picking the daily number (order matters so nPr)

if we box the number (order does not matter so nCr)

The difference is if order matters or not.