Question

Evaluate. 5!4! = [?]

Answer 1

The Answer Is One.
Because I Learn !=meaning (-)

Answer 2

Answer:

2880

Step-by-step explanation:

!

in mathematics means factorial.

What is factorial?

Factorial is the product of an integer and all below it to  

1

n

!

=

n

⋅

(

n

−

1

)

!

for  

n

≥

1

or simply  

n

!

=

1

⋅

2

⋅

3

⋅

...

n

Notice that  

0

!

is defined as  

1

by mathematicians as it is the empty product.

So for  

5

!

, we have

5

!

=

5

⋅

(

5

−

1

)

!

 

⇒

5

!

=

5

⋅

4

!

5

!

=

5

⋅

4

⋅

(

4

−

1

)

!

 

⇒

5

!

=

5

⋅

4

⋅

3

!

5

!

=

5

⋅

4

⋅

3

⋅

(

3

−

1

)

!

 

⇒

5

!

=

5

⋅

4

⋅

3

⋅

2

!

5

!

=

5

⋅

4

⋅

3

⋅

2

⋅

(

2

−

1

)

!

 

⇒

51

=

5

⋅

4

⋅

3

⋅

2

⋅

1

!

But,  

1

!

=

1

⋅

(

1

−

1

)

!

Which is  

1

!

=

1

⋅

0

!

and  

0

!

=

1

Finally,

⇒

5

!

=

5

⋅

4

⋅

3

⋅

2

⋅

1

That is the pattern, so  

n

!

=

n

⋅

(

n

−

1

)

!

 

...

1

!

until you get to  

1

!

Or simply;  

n

!

=

1

⋅

2

⋅

3

⋅

...

n

∴

5

!

4

!

=

(

5

⋅

4

⋅

3

⋅

2

⋅

1

)

⋅

(

4

⋅

3

⋅

2

⋅

1

)

⇒

120

⋅

24

=

2880