A permutation is mathematical statement that is illustrated by nPr and that you will use if order matters. In order to fully understand this you will need to know what a factorial is. A factorial is a whole number multiplied by the previous number by 1 and so on; example: 9! = 9*8*7*6*5*4*3*2*1 = 362,880. As you now know a permutation is represented by nPr and its actual equation is n!/(n-r)!. With this knowledge we can now do an example: 10P4 = 10!/(10-4)! = 10!/6! = 10*9*8*7 = 5,040 different possibilities.
A combination however is slightly different and isnt quite the same as nPr, but is in the sense that is illustrated by nCr which can sometimes get confusing. Lets plug the same numbers into a combination notation and see if these numbers turn out the same: 10C4 = 10!/(10-4)!4! = 10!/(6*5*4*3*2*1) 4! = 10*9*8*7*6*5*4*3*2*1/720*24 = 3,628,800/2,880 = 1,260 different possibilities. Wow! That isnt quite the same at all now is it? Lets take a look back at the equation, as thats where the difference between them lies. If you noticed this is why we get different answers between them; nPr = n!/(n-r)! while nCr = n!/(n-r)! r!