we will discuss some basic ideas of
Permutation and Combination Methods . On the basis of these ideas we will learn trick and tips of shortcut permutation and combination. If you think that how to solve permutation and combination questions using permutation and combination shortcut tricks , then further studies will help you to do so.
General Rule and Formula
Permutation and combination methods related math calculation are given in bank exams so its important to learn for exams.
Factorial Notation
If we consider that ‘ n ‘ be a positive integer. Then, we denoted factorial n as ⌊n or n! .
n! is defined as
n! = n (n-1) (n-2) …………….3.2.1.
Example
5! = ( 1 x 2 x 3 x 4 x 5 )
5! = 120.
4! = ( 1 x 2 x 3 x 4 )
4! = 24.
3! = ( 1 x 2 x 3 )
3! = 6.
Things to Remember
Permutation
The different arrangements of a given number or things by taking some or all at a time, are called Permutations.
In Short and basic think, permutation is arrangement, given number or letter, that how we arrange it. we can arrange it taking some number or letter at a time or we can arrange it taking all at a time.
Example
All permutations (or arrangements) made with the letters of a, b, c by taking two at a time are ( ab, ba, ac, ca, bc, cb ).
Example
All permutations made with the letters a, b, c, taking all at a time are : ( abc, acb, bac, bca, cab, cba ).
Number of Permutations
Number of all permutations of n things, taken r at a time, is given by:
P = n (n-1) (n-2)……(n-r+1)
OR
P = n! / (n-r)!
Example
P
5! / (5-2)!
= 5! / 3!
= ( 5 x 4 x 3 x 2 x 1 ) / ( 3 x 2 x 1 )
= ( 5 x 4 )
= 20.
Example
P
8! / (8-3)!
= 8! / 5!
= ( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) / ( 5 x 4 x 3 x 2 x 1 )
= ( 8 x 7 x 6 )
= 336.
Step 1: Figure out if you have
permutations or combinations. You
can't just throw people into these
positions; They are selected in a
particular order for particular jobs.
Therefore, it's a permutations problem.
Step 2: Put your numbers into the
formula.
Let me try to explain Permutations first !!Permutation means all possible arrangements of Number, letter or any other product or things etc.
Before understanding the meaning of Permutation let us first understand why do we need to understand it? Is it have any practical implicationin our life? Of course yes!!
Let me explain.
Our beloved joker is getting bored hence he is going to plan bank robbery He is planning to enter near the bank main safe at Sunday night 9PM when Bank is closed.
Mind it Bank will open and all the bank employees will come at 9 am Monday morning.
That is pretty much time for our joker? Isn’t it?
Complete 12 hours to crack the code of main safe.
Oh But what happened here? Why our joker is crying? It is just 9 digit code which he need to crack and he has 12 hours to do that.
What is stopping him to finish his job?
Mathematics!! Can Mathematics stop him to do his job? Yes!!
I think he has not studied permutation in his math classes.
1 2 3 4 5 6 7 8 9 these 9 digits can have following arrangements lets assume repetion is not allowed9! = 1×2×3×4×5×6×7×8×9= 362880 (We will explain the formula in detail in next lecture).
SO basically our Joker may has to try up to 362880 different arrangement for cracking the bank safe!!!If he spent just one second for trying one arrangement let’s say 234567918 it means he has to spend 362880 seconds for trying all the arrangements.
Which means 6048 Minutes! Which means 100.8 hours Which means 4.2 days nonstop working!!If we include little Nap, Food and bathroom activity it’s approximately 5 days of work!!
1 month ago
Permutation and Combination Methods . On the basis of these ideas we will learn trick and tips of shortcut permutation and combination. If you think that how to solve permutation and combination questions using permutation and combination shortcut tricks , then further studies will help you to do so.
General Rule and Formula
Permutation and combination methods related math calculation are given in bank exams so its important to learn for exams.
Factorial Notation
If we consider that ‘ n ‘ be a positive integer. Then, we denoted factorial n as ⌊n or n! .
n! is defined as
n! = n (n-1) (n-2) …………….3.2.1.
Example
5! = ( 1 x 2 x 3 x 4 x 5 )
5! = 120.
4! = ( 1 x 2 x 3 x 4 )
4! = 24.
3! = ( 1 x 2 x 3 )
3! = 6.
Things to Remember
Permutation
The different arrangements of a given number or things by taking some or all at a time, are called Permutations.
In Short and basic think, permutation is arrangement, given number or letter, that how we arrange it. we can arrange it taking some number or letter at a time or we can arrange it taking all at a time.
Example
All permutations (or arrangements) made with the letters of a, b, c by taking two at a time are ( ab, ba, ac, ca, bc, cb ).
Example
All permutations made with the letters a, b, c, taking all at a time are : ( abc, acb, bac, bca, cab, cba ).
Number of Permutations
Number of all permutations of n things, taken r at a time, is given by:
P = n (n-1) (n-2)……(n-r+1)
OR
P = n! / (n-r)!
Example
P
5! / (5-2)!
= 5! / 3!
= ( 5 x 4 x 3 x 2 x 1 ) / ( 3 x 2 x 1 )
= ( 5 x 4 )
= 20.
Example
P
8! / (8-3)!
= 8! / 5!
= ( 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ) / ( 5 x 4 x 3 x 2 x 1 )
= ( 8 x 7 x 6 )
= 336.