Permutation vs. combination vs arrangement

Bumping this up because the first answer wasn't satisfactory, and I was studying it myself...

-Combination is the selection of a group from a number of items, or people. There is a group which is selected and a group not selected, and so the formula nCr has the number selected and number unselected dividing the total number. Order is without significance.
\(\frac{n!}{r!(n-r)!}\)

-Permutation is the arragement of a group from a number of items, or people. There is a group which is selected AND ordered, and the formula nPr has the number of unselected dividing the total number. The order of the items, or people, selected are what concerns us, and therefore the unselected is cleared out.
\(\frac{n!}{(n-r)!}\)

Tip:
-If you are working from selection and the solution is required without order, divide by the number of which are not to be ordered. That said, the reverse is true too; if you are working from an ordered solution, multiply by number of items selected to unarrage them.
-Slot method is a way of setting up a problem, and it is used for both combination and permutations, selections and arrangements, respectively.
-Arragement is what the problem is asking for, but permutation is the standard formula to solve it.