Question Number 43344 by peter frank last updated on 10/Sep/18
$$\mathrm{The}\:\mathrm{number}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:{n}\:\:\mathrm{are}\:\mathrm{arranged} \\ $$ $$\mathrm{in}\:\mathrm{a}\:\mathrm{random}\:\mathrm{order}.\:\mathrm{The}\:\mathrm{probability} \\ $$ $$\mathrm{that}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:...,\:{k}\:\left({k}>{n}\right)\:\mathrm{appears} \\ $$ $$\mathrm{as}\:\mathrm{neighbours}\:\mathrm{is} \\ $$
Commented byMrW3 last updated on 10/Sep/18
$${k}<{n} \\ $$ $$\frac{\left({n}−{k}+\mathrm{1}\right)!{k}!}{{n}!} \\ $$