MathDB
Problems
Contests
National and Regional Contests
India Contests
Mathematics Talent Reward Programme (MTRP)
2018 Mathematical Talent Reward Programme
MCQ: P 7
How many functions f: A-> A are there such that f(1)<f(2)<f(3)
How many functions f: A-> A are there such that f(1)<f(2)<f(3)
Source:
February 17, 2021
function
algebra
Problem Statement
A
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
.
A=\{1,2,3,4,5,6,7,8\} .
A
=
{
1
,
2
,
3
,
4
,
5
,
6
,
7
,
8
}
.
How many functions
f
:
A
→
A
f: A \rightarrow A
f
:
A
→
A
are there such that
f
(
1
)
<
f
(
2
)
<
f
(
3
)
f(1)<f(2)<f(3)
f
(
1
)
<
f
(
2
)
<
f
(
3
)
[*]
(
8
3
)
{{8}\choose{3}}
(
3
8
)
[*]
(
8
3
)
5
8
{{8}\choose{3}}5^{8}
(
3
8
)
5
8
[*]
(
8
3
)
8
5
{{8}\choose{3}} 8^{5}
(
3
8
)
8
5
[*]
8
!
3
!
\frac{8 !}{3 !}
3
!
8
!
Back to Problems
View on AoPS