What is factorial ?
Factorial is a very simple term and an interesting term .
First of all let’s see the interesting sing of factorial …
“ ! “
Factorial is the multiplication of whole numbers from our chosen number down to 1 .
For example , suppose your chosen number is 5 . then what is the factorial of 5 ?
Yes that will be 5!
From definition, we can write it ,
5! = product of whole numbers from our chosen number down to 1 .
Like this ,
1) What will be the 6! ?
This will be = 6 X 5 X 4 X 3 X 2 X 1 =720
2) What will be the 10! ?
Ans : This will be 10! = 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1.
Here is an interesting thing, we can write an factorial number using another factorial .
Such as , we know 4! = 4 X 3 X 2 X 1.
And 5! = 5 X 4 X 3 X 2 X 1.
See this two factorial number carefully . here in 5! and 4! the common term is ( 4 X 3 X 2 X 1 ) which is the factorial of 4.
So we can write 5! = 5 X 4! .
More example :
1) 6! = 6 X 5 X 4 X 3 X 2 X 1
And 5 ! = 5 X 4 X 3 X 2 X 1.
So from this two factorial number we can write -
6! = 6 X 5!
2) 10 ! = 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1.
We can write It , 10! = 10 X 9!
Because 10 ! = 10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 from 9 to 1 is the part of 9!.
So just mind a trick, that is every number factorial value is the product of the number itself and its previous number factorial.
For factorial method , we can apply a formula that is
n! = n ( n- 1 )!
Here n is the chosen number .
So ,if chosen number is 7 then ,
7! = 7 X ( 7 - 1 )! = 7 X 6 !
Some more example :
1) 100! = 100 X 99!
2) 125! = 125 X 124! ans so on.
Lets know about “ 0 ! “
One of the most interesting factorial is 0!. the the ans of the 0! is always 1 .
Why 0! means 1 before explaining it I will explain an interesting things .
1) Suppose you have thee cards written with a,b,c . If I ask you how many ways can we arrange these letters without repeating .
You will must arrange like this >>
1. abc,
2. acb,
3. bac,
4. bca,
5. cab,
6. Cba
The ans is in 6 ways .
Yes its right .
>> If there have 2 letters a and b .then how many ways can we arrange these letters without repeating ?
You can arrange this ,
1) ab
2) ba
Ans is “ 2 ” ways .
>> If says,you have now 10 letters a,b,c,d,e,f,g,h,I,h . then how many times you can arrange them without repeating ?
If you would like to arrange them you can arrange them but it will take much time to find out the result .
So how to solve it?
Yes see the first math where letter was 3 result was 6 .
Here 3 is out chosen number
We can write it 3 ! = 3 X 2 X 1 = 6 .
In the second math there had 2 letters and ans was 2 .
Here 2 is out chosen number
We can write it 2! = 2 X 1 = 2
And now what will be the ans for arranging of 10 letters . you don’t need to wast your time to arranging them to find out the result . you can shortly do this .
The result will be 10! = 3,628,800
So, now just make a sense, if we say you have 0 letters and how can we arrange letters without repeating?
Then the result will be 0! . but if there have not any number how you can arrange no lattes or numbers? We can't arrange them but there have an empty result.Nothing means empty .
And empty is the result means there have only one result . so the factorial of 0 is 1
0! = 1.
May be this will helpful for you .
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