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Math Prize For Girls Problems
2016 Math Prize for Girls Problems
5
5
Part of
2016 Math Prize for Girls Problems
Problems
(1)
Math Prize 2016 Problem 5
Source:
9/12/2016
A permutation of a finite set
S
S
S
is a one-to-one function from
S
S
S
to
S
S
S
. A permutation
P
P
P
of the set
{
1
,
2
,
3
,
4
,
5
}
\{ 1, 2, 3, 4, 5 \}
{
1
,
2
,
3
,
4
,
5
}
is called a W-permutation if
P
(
1
)
>
P
(
2
)
<
P
(
3
)
>
P
(
4
)
<
P
(
5
)
P(1) > P(2) < P(3) > P(4) < P(5)
P
(
1
)
>
P
(
2
)
<
P
(
3
)
>
P
(
4
)
<
P
(
5
)
. A permutation of the set
{
1
,
2
,
3
,
4
,
5
}
\{1, 2, 3, 4, 5 \}
{
1
,
2
,
3
,
4
,
5
}
is selected at random. Compute the probability that it is a W-permutation.
Math Prize for Girls