Permutations & Combinations

Assuming that you teach three students namely a,b,c. It so happens with them they come in a group of two each day.
Hence, they can keep you busy by coming in a group of two each day say (a,b),(b,c), (c,a) i.e., only three ways.
But if you keep a watch on their movements in your class and also observe the order they enter your class then it would amount to 6 ways viz. (ab), (ba), (ca), (ac), (bc),(cb).

Combinations: If the order does not matter in an arrangement i.e., we would have three combinations of groups consisting of two each i.e., (a,b), (b,c), (c,a)
Here the order within each set selected does not matter.

Permutations: If three items a,b,c, were to be arranged in groups of two, there would be six arrangements i.e., (a,b), (b,a), (c,a), (a,c), (b,c),(c,b).
Notice that an order within each combination does not matter while in Permutation it does.

Some Rules covering Permutations & Combinations
If there are 'm' ways of one arrangements and 'n' ways of another then there are total of 'm.n' ways
the number of ways of arranging n different things taken all of them at a time is n! or [n] ways
the number of ways of arranging 'n' different things taken only 'r' at a time is n P r or = (n) (n - 1) (n - 2) …. (n - r + 1) ways
The number of permutations of 'n' dissimilar things taken 'r' at a time is n.n.n.n…….r times
If we consider 'n' items in a Circular arrangements then this can be done in [n-1] ways