Permutation and Combination Shortcut Tricks

Assume that I have 4 letters (A, B, C and D). Now if anybody asks me to write down all the permutations of 3 of these letters…..
 

So, there are 24 permutations in total. Here the order is important. In other words ACB is different, BCA is different, CBA is different and ABC is different (even-though they all are formed with same group letters).

As we have already discussed, the collection of letters is important here, not the order. That means, if you have ABC in your set that’s enough. So you cant claim ABC, ACB, BAC, BCA, CAB, CBA… for combinations. These all are 1 combination of letters A, B and C.

So, from the given 4 letters (A, B, C and D), You can write the combination of 3 of those letters

  

Now lets have a look at the technical side, before going to calculate Permutations and Combinations, you should know the word Factorial.

Factorial : The factorial of a number, represented by n!, is the product of the natural numbers up to and including n

In simple words, the Factorial of thenumber n is the number of ways that the n elements of a group can be ordered.
So, if somebody ask you a question,how many different ways six people can sit at a table with six chairs,
you should say them its 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.

Note : We treat 0! as 1

There is a simple formula for calculating permutations.

Number of all permutations of nitems, taken r at a time, is given by:

n above case n is 4 and r is 3

So, ⁿP_r = P(n,r) = 24