Answer:
This can be done using the choose function.
The number of combinations are given by:
(
n
k
)
=
n
!
k
!
(
n
−
k
)
!
where
n
is the total number of students and
k
is the number of students to be picked. So we have
n
=
20
and
k
=
5
:
(
20
5
)
=
20
!
5
!
(
20
−
5
)
!
=
20
!
5
!
15
!
Evaluate directly with a calculator:
20
!
5
!
15
!
=
15504
we can simplify this before calculation by hand:
20
!
5
!
15
!
=
20
×
19
×
...
×
2
×
1
5
×
4
×
3
×
2
×
1
×
(
15
×
...
×
1
)
=
(
20
×
...
×
16
)
(
15
×
...
×
1
)
(
5
×
...
×
1
)
(
15
×
...
×
1
)
=
(
20
×
...
×
16
)
15
×
...
×
1
(
5
×
...
×
1
)
15
×
...
×
1
=
(
20
×
19
×
18
×
17
×
16
)
(
5
×
4
×
3
×
2
×
1
)
Simplify the numbers matched up by color:
=
(
4
×
19
×
9
×
17
×
4
)
(
1
×
1
×
3
×
1
×
1
)
=
(
4
×
19
×
3
×
17
×
4
)
(
1
×
1
×
1
×
1
×
1
)
=
3
×
4
×
4
×
17
×
19
=
48
×
323
=
15504