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 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 ?

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

The number of circular permutations of 8 things taken 4 at a time is

The number of circular permutation of 8 things taken 4 at a time is

The number of circular permutations of 8 things taken 4 at a time is

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

2.The number of permutations of 8 things taken at a time is 1680, Then r=

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