MathDB

2022 Combinatorics 10

Source:

March 18, 2022

probabilitycombinatorics

Problem Statement

Let

S

be a set of size

11

. A random

12

-tuple

(s_1, s_2, . . . , s_{12})

of elements of

S

is chosen uniformly at random. Moreover, let

\pi : S \to S

be a permutation of

S

chosen uniformly at random. The probability that

s_{i+1}\ne \pi (s_i)

for all

1 \le i \le 12

(where

s_{13} = s_1

) can be written as

\frac{a}{b}

where

a

and

b

are relatively prime positive integers. Compute

a

.

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