In how many of the permutations of 12 things taken 3 at time will one particular thing (a) always occur (b) never occur ?

In how many of the permutations of 12 things taken 6 at a time will 3 particular things (a) always occur b) never occur ?

In how many permutations of 11 dissimilar things, taken 4 at a time, will one particular thing always occur?

In how many of the permutations of n things taken r at a time will 5 things (i) always occur, (ii) never occur ?

In how many of the permutations of 10 things taken 4 at a time will (i) on thing always occur,(ii) never occur ?

Find the number of permutations of n things taken r at a time in which two particular things : (i) always occur (ii) never occur.

The number of permutations of n things taken r at a time if 3 particular things always occur is

The number of permutations of n things taken r at a time if 3 particular things always occur is

In how many of the permutations of n thing taken r at a time will three given things occur?

In how many of the permutations of n thing taken r at a time will three given things occur?

In how many of the permutations of n thing taken r at a time will three given things occur?