Find the number of permutations of n things, taken r at a time, in which 3 particular things : always occur.

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

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

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

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 .

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are : included .

Find the number of permutations of 12 things, taken 6 at a time, in which 3 particular things are : excluded .

Find the number of permutations of n different things taken r at a time such that 3 specific things occur together ?

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=182b c , find the value of xdot a) 10 b) 12 c) 15 d) 18

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=182b c , find the value of xdot