Factorial


 
 
Concept Explanation
 

Factorial

Factorial

The continued product of first n natural numbers is called the "n factorial" and is denoted by n!

i.e.    n! = 1 X 2 X 3 X 4 X ... X ( n- 1) X n.

Thus,  3! = 1 X 2 X 3 = 6;

4! = 1 X 2 X 3 X 4 = 24,

5! = 1 X 2 X 3 X 4 X 5  = 120 etc.

Clearly, n! is defined for positive integers only.

Zero Factorial:

To find factorial of 0 We can multiply the integers from 1 to zero because multiplication of 0 is not defined.

So, we define 0! = 1.

Factorial of proper fractions or negative integers are not defined.

Hence we can say that factorial n is defined only for whole numbers.

                  n! = 1 X 2 X 3 X 4... X (n - 1) X n

Rightarrow              n! = [ 1 X 2 X 3 X 4...X (n - 1)] X n

Rightarrow               n! = [( n- 1)!] n = n X ( n - 1) !

Thus,           n! = n X ( n - 1) !

For example,

8! = 8.(7!)

5! = 5.(4!)

3! = 3.(2!)

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Sample Questions
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Question : 1

Compute factorial of 9

Right Option : B
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Explanation
Question : 2

Compute the following expression

frac{18!}{15! 4!}

Right Option : D
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Explanation
Question : 3

Compute the following expression

 frac{10!}{5! 3!}

Right Option : A
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Explanation
 
 


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