2. 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 permutations of n things taken r at a time if 3 particular things always occur is

If a denotes the number of permutations of (x+2) things taken all at a time,b the number of permutations of x things taken 11 at a time and c the number of permutations of x-11 things taken all at a time such that a=182bc, find the value of x.

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

Find the number of permutations of n things, taken r at a time, in which 3 particular things : (i) always occur (ii) will never occur.

Find the number of permutations of 7 objects, taken 3 at a time.

The number of permutations of n different things taking r at a time when 3 particular things are to be included is ^(n-3)P_(r-3) b.n-3P_(r) c.^(n)P_(r-3) d.r!^(n-3)C_(r-3)