Question

In how many permutation of $11$ dissimilar things, takes $4$ at a time, will one particular thing
(a) always occur?
(b) never occur?

Answer 1

a

4 out of 11 things and one of them always occurs

${}^{10}{P}_3\times 4=720\times 4=2880$

b

4 out of 10 things, as one will never occur

${}^{10}{P}_4=5040$