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India Contests
ISI Entrance Examination
2020 ISI Entrance Examination
8
8
Part of
2020 ISI Entrance Examination
Problems
(1)
ISI 2020 : Problem 8
Source: B.Stat & B.Math Entrance Exam 2020
9/20/2020
A finite sequence of numbers
(
a
1
,
⋯
,
a
n
)
(a_1,\cdots,a_n)
(
a
1
,
⋯
,
a
n
)
is said to be alternating if
a
1
>
a
2
,
a
2
<
a
3
,
a
3
>
a
4
,
a
4
<
a
5
,
⋯
a_1>a_2~,~a_2<a_3~,~a_3>a_4~,~a_4<a_5~,~\cdots
a
1
>
a
2
,
a
2
<
a
3
,
a
3
>
a
4
,
a
4
<
a
5
,
⋯
or
a
1
<
a
2
,
a
2
>
a
3
,
a
3
<
a
4
,
a
4
>
a
5
,
⋯
\text{or ~}~~a_1<a_2~,~a_2>a_3~,~a_3<a_4~,~a_4>a_5~,~\cdots
or
a
1
<
a
2
,
a
2
>
a
3
,
a
3
<
a
4
,
a
4
>
a
5
,
⋯
How many alternating sequences of length
5
5
5
, with distinct numbers
a
1
,
⋯
,
a
5
a_1,\cdots,a_5
a
1
,
⋯
,
a
5
can be formed such that
a
i
∈
{
1
,
2
,
⋯
,
20
}
a_i\in\{1,2,\cdots,20\}
a
i
∈
{
1
,
2
,
⋯
,
20
}
for
i
=
1
,
⋯
,
5
i=1,\cdots,5
i
=
1
,
⋯
,
5
?
isi
2020