Introduction: Permutations and Combination:

Permutations:
Permutations are the different arrangements of a given number of things by taking some or all at a time.

Examples
All permutations (or arrangements) that can be formed with the letters a, b, c by taking three at a time are (abc, acb, bac, bca, cab, cba)
All permutations (or arrangements) that can be formed with the letters a, b, c by taking two at a time are (ab, ac, ba, bc, ca, cb)
The number of permutations of n objects taken r at a time is determined by the following formula:
P(n,r)=n!/(n−r)!

Combinations:
Each of the different groups or selections formed by taking some or all of a number of objects is called a combination.

Examples:
Suppose we want to select two out of three girls P, Q, R. Then, possible combinations are PQ, QR, and RP. (Note that PQ and QP represent the same selection.)
Suppose we want to select three out of three girls P, Q, R. Then, the only possible combination is PQR
The number of Combinations of n objects taken r at a time is determined by the following formula:
nCr = n! / [r! * (n-r)!]

Repetition:
The term repetition is very important in permutations and combinations. Consider the same situation described above where we need to find out the total number of possible samples of two objects which can be taken from three objects P, Q, R.
If repetition is allowed, the same object can be taken more than once to make a sample. i.e., PP, QQ, RR can also be considered as possible samples.
If repetition is not allowed, then PP, QQ, RR cannot be considered as possible samples