clancy the best way is below:
If the order doesn't matter, it is a combination.
I.e. How many possible ways can 10 people sit in 3 chairs?
Instead of doing a sloppy mess with the n! R! And all that other junk!! Do it this way:
(10*9*8) / 3! = 240
the reason why you do 10*9*8 is because thats the highest values going to the lowest and you stop at 8 because you only need 3 chairs, but since order does not matter you have to divided by factorial of the # of necessary chairs i.e. 3! In this case.
Try this it works all the time!
If the order
does matter it is a permutation.
I.e. Out of 5 people how many can ways can there be vice president, president, director (selected in that order)
answer: 5*4*3 = 60
again you have 5 people, but order matters because you cannot reselect a person to be another position, therefore you take your total 5
and then multiple by 4*3 (again since there are only 3 total positions) but since order matters, you do not divide here!
Thats it! No kaka dudu formulas! This works all the time! Try it for yourself, the only time it wont work is if you confuse order matters for order doesnt matter; which is easy to do so be careful!
I never do the formulas anymore because this way is logical and less confusing as long as you know whether its a permutation or combination.