Hello everyone, welcome back to our new video
In today's video, we are going to do a new and fresh topic
that is Permutation and Combination
You must have heard this name many times
I mean, in your normal life also you must have heard the
word combination many times So, what are these two? and
what is the difference between these two? we will know that
in today's video So, Permutation and Combination
Combination means Selection
If we are selecting something it means we are asking about
the combination
If we are asking about the selection of something it means
we are asking about the combination
But, if we select the same thing
Now, if we have to arrange it
So, Selection plus if we arrange it then it will be called
as Permutation
That is, first of all, we will have Selection of things
Then, afterwards, we will arrange those things
So, this will be our Permutation I will explain you about
these two with a simple example
Let us suppose we have digits We have digits
From where to where?
We have digits from 0, 1, 2, 3 and till 9 These are our 10
digits
Now, what we have to do with the help of these digits?
We have to make a PIN code with the help of these digits
What is PIN?
We have to make a PIN with the help of these digits Now,
how many digits does a PIN have? We have only 4 digits
We have a PIN of 4 digits
So, if we have to make a 4 digit PIN
So, what we will do first?
First of all, we will select 4 digits from these 10 digits
Now, if we are selecting 4 digits So, what will come for
select?
The thing which will come for select will be Combination
So, the formula for Combination is NCR This is your formula
for Combination
Capital C represents Combination
Nothing else
Small n represents the total number of objects For example,
we have total number of objects
Total number of objects is 10
We have to select from 10 digits So, total number of
objects will be N
In this case, it will be 10
R will be the number of objects which we have to select
Which are required So, R will be the number of objects
which we have to select So, how many objects we have to
select from N objects?
R objects
Selecting R objects from N objects This is its indirect
meaning
Now, if we have 10 objects
How many objects we have to select from it?
Only 4
So, what will be the formula for Combination? 10CR Now, 10CR
I have just told you the representation Not 10CR
R also has a value
That is 4
So, 10C4
Means, we have total 10 digits
And how many objects we have to select from it?
We have to select 4 digits
I have just told you the representation What will be the
formula for it? I will tell you later
So, we have selected 4 digits from 10CR
It can be any 4 random digits Now, if we have to make pin
from it
Then 4 random digits
Let us suppose, it is 1, 5, 7, 9 Now, if we are creating
pin from it So, if we make pin 1, 7, 9
Or we make pin 1, 5, 9, 7
Are both the pins different or not? Obviously, both the
pins are different
If one digit is also moved forward and backward
Then we will get one different pin
So, what is this?
This is called arrangement
Means, what is happening to us from the arrangement of the
digits? There is a difference in it
So, there was no difference in the selection That we have
to select any 4 digits
But, when it came to arranging them Then what happened to
us?
We started getting difference
We started getting different pins
So, when this arrangement comes
Then what happens to us?
It becomes a case of permutation
So, how many arrangements will we get in this? First of
all, we will select 4 digits So, for selection, we will
have same formula NCR What formula will we have for
selection? For selection, we will have formula NCR only
Now, what will be the formula for arrangement? For
arrangement, we have 4 places And we have 4 digits to place
here
We have 4 digits to place on these 4 places
So, which digits can be placed here? Any one digit can be
placed from 1, 5, 7, 9
So, any one digit can be placed So, how many choices do we
have to fill this place?
We have 4 choices to fill this place Now, the pin which you
have to create There is a condition in it
That the number which is used once It cannot be used again
So, it cannot be used again
So, the number which will come on 2nd place
We have only 1 choice left
We can put any other 3 numbers other than 1
So, for 2nd place, we have 3 choices
So, we can fill it in 3 ways
We can put 5, 7 or 9 Similarly, one digit is used here
One digit is used here
How many choices are left for this side?
Only 2 choices And for this side, only 1 choice is left
So, now we have to find out the permutation What will
happen? Multiply these
So, what will happen?
When we get this type of sequence That is, the number is
reduced one by one till 1
And these are multiplying
So, we will call this as 4 factorial
So, now multiply 4 factorial in ncr
So, what will happen?
The formula of permutation will come
That is equal to npr
Because we are taking out npr for permutation So, what will
be the formula of npr? ncr into 4 factorial
What is 4 factorial?
Whose value was 4?
It was r value
Because the number of objects which we were picking
That was r and that is 4 So, this will be npr
Is equal to ncr into r factorial I hope you will get to
know the difference between these two from this example
And you will also get to know the relation between these
two In the next video, we will study the concepts and
formulas
And we will ask questions
Till then keep practicing
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