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

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

Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always : included .

Find the number of permutations of 8 things, taken 3 at a time, in which 2 particular things are always : excluded .

If six times the number of permutations of n things taken 3 at a time is equal to seven times the number of permutations of (n-1) things chosen 3 at a time, find n.

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.

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