Question

How many of the permutations of 10 different things taken 4 at a time with one particular thing : (a) Never occur (b) Always occur.

Answer 1

a)
Out of 10 different things one thing never occur then 4 things will be occur out of 9 things.
Therefore,

9p4=(9!)/(9-4)!

=(9*8*7*6)

=3024

b)

Here, if 1 thing always occur then we will fix that place. Now 3 places are remaining and 9 things are remaining.

4*(10–1 p 3)

= 4* (9 p 3)

= 4*9*8*7

=2016.