What is the cardinality of the set\{f\mid f : [7]\rightarrow[7],\ f is a biject

Albarellak

Albarellak

Answered question

2021-08-16

What is the cardinality of the set
{ff:[7][7], f is a bijectioon such that f(i)i, for every i={1, 2, 3, 4, 5, 6, 7}?

Answer & Explanation

Khribechy

Khribechy

Skilled2021-08-17Added 100 answers

Step 1
f(i)ii
f is a derangement on 7 letters
Number of derangements on n letter
=Dn={n}(11{1}+1{2}1{3}++(1)n{n})
D7={7}(11{1}+1{2}1{3}+1{4}1{5}+1{6}1{7})
=0+2520840+21042+71
=1854

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Discrete math

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?