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Aman Bansal
592 Points
9 years ago

Dear Simrandeep,

Permutation Permutation means arrangement of things. The word arrangement is used, if the order of thingsis considered.

CombinationCombination means selection of things. The word selection is used, when the order of things hasno importance.

Example:     Suppose we have to form a number of consisting of three digits using the digits 1,2,3,4, To form this number the digits have to be arranged. Different numbers will get formed depending upon the order in which we arrange the digits. This is an example of Permutation.

Now suppose that we have to make a team of 11 players out of 20 players, This is an example of combination, because the order of players in the team will not result in a change in the team. No matter in which order we list out the players the team will remain the same! For a different team to be formed at least one player will have to be changed.

Now let us look at two fundamental principles of counting:

Addition rule : If an experiment can be performed in ‘n’ ways, & another experiment can be performed in ‘m’ ways then either of the two experiments can be performed in (m+n) ways. This rule can be extended to any finite number of experiments.

Example:       Suppose there are 3 doors in a room, 2 on one side and 1 on other side. A man want to go out from the room. Obviously he has ‘3’ options for it. He can come out by door ‘A’ or door ‘B’ or door ’C’.

Multiplication Rule : If a work can be done in m ways, another work can be done in ‘n’ ways, then both of the operations can be performed in m x n ways. It can be extended to any finite number of operations.

Example.:      Suppose a man wants to cross-out a room, which has 2 doors on one side and 1 door on other site. He has  2 x 1  = 2 ways for it.

Factorial n : The product of first ‘n’ natural numbers is denoted by n!.

n!   = n(n-1) (n-2) ………………..3.2.1.

Ex.       5! = 5 x 4 x 3 x 2 x 1 =120

Note       0!     =  1

Proof   n! =n, (n-1)!

Or           (n-1)! = [n x (n-1)!]/n = n! /n

Putting n = 1, we have

O!  = 1!/1

or  0 = 1

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Aman Bansal

Aman Bansal
592 Points
8 years ago

Dear Kurma,

Mathematics we use more precise language:

 If the order doesnt matter, it is a Combination. If the order does matter it is a Permutation.

 So, we should really call this a "Permutation Lock"!

Cracking IIT just got more exciting,It s not just all about getting assistance from IITians, alongside Target Achievement and Rewards play an important role. ASKIITIANS has it all for you, wherein you get assistance only from IITians for your preparation and win by answering queries in the discussion forums. Reward points 5 + 15 for all those who upload their pic and download the ASKIITIANS Toolbar, just a simple  to download the toolbar….

So start the brain storming…. become a leader with Elite Expert League ASKIITIANS

Thanks

Aman Bansal