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
