No. of circular permutations of 15 things taken 5 at a time in one direction is:

Number of circular permutations of 15 things taken 5 at a time in one direction is

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

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

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 7 dissimilar things taken 5 at a time is

Find the number of permutations of 20 things taken 5 at a time so that one particular thing will always occur

Find the number of permutations of 20 things taken 5 at a time so that one particular thing will 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 ?

Find the number of permutations of n things taken r at a time in which two particular things : always occur.