Permutation (arrangement of objects):

The number of permutations of n distinct objects, taken r at a time, is the total number of arrangements of r elements, chosen from n objects where the order of the arrangement is very important. Arranging n different objects, taken r at a time is similar to filling r places from n objects.

The number of types of arranging = The number of types of filling r places

(b) The number of arrangements of n separate things taken all at a time = ⁿp_n = n!

Combination:

Meaning of combination is choice of objects. 

Choices of objects without repetition:

The number of choices (combinations or groups) that may be created from n different objects taken r (0 ≤ r ≤ n) at a time is 

Choices of objects with repetition:

The number of combinations of n different objects, taken r at a time when each can occur once, twice, thrice,..... upto r times in any combination is ⁿH_r = ^n+r-1C_r .

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