Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Grinstead-Snell-Probability
· Problem 3.3.2
Conditional Probability
Mathematics · card-shuffling-probability
Problem
Show that if we start with the identity ordering of
{
1
,
2
,
…
,
n
}
\{1, 2, \ldots, n\}
{
1
,
2
,
…
,
n
}
, then the probability that an
a
a
a
-shuffle leads to an ordering with exactly
r
r
r
rising sequences equals
(
n
+
a
−
r
n
)
a
n
A
(
n
,
r
)
,
\frac{\binom{n+a-r}{n}}{a^n} A(n, r),
a
n
(
n
n
+
a
−
r
)
A
(
n
,
r
)
,
for
1
≤
r
≤
a
1 \leq r \leq a
1
≤
r
≤
a
.
Browse the problem library